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THE 
LONDON, EDINBURGH, akd DUBLIN 

PHILOSOPHICAL MAGAZINE 

AND 

JOURNAL OF SCIENCE. 

CONDUCTED BY 

SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. 
SIR WILLIAM THOMSON, Kkt. LL.D. F.R.S. Ac. 

AND 

WILLIAM FRANCIS, Ph.D. F.L.S. F.R.A.S. F.C.S. 



" Nee aranearum sane lextoi ideo melior quia ex le fila gignunt, nee noster 
Tifior quia ex alieni* libamiu nt apea." Jcar. Lifs. Pelil. lib. i. cap. 1 . Kot. 



VOL. v.— FIFTH SERIES. 
JANUARY— JUNE 1878. 

TATLOB AND ^ULNCIS, "EED LION OOUBT, FLEET STEEET. 

SOLD BT LOHOIIANS, GREEIT, BXADBB, AND DYER; KENT ASD CO. ; 8IMPKIK, MARSHALL 

A5D CO. ; AJf D WniTTAKBR ABD CO. ; — AND BY ADAM AND CHARLES BLACK, 

AJfD THOMAS CLABK, EDINBURGH ; SMITH AND BON, GLASGOW ; — 

HODGES, POSTER, A5D CO, DUBLIB ; — PUTHAM, KEW 

YORK ;— AND A8HER AND CO., BERUN. 



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'' Meditationis est perscrutari occulta; contemplationis est admiiaii 

perspicua Admiratio generat quaestionem, quceatio inyestigationem, 

inyestigatio inyentionem." — Buffo de S. Victore, 



— " Cur Spirent venti, cur terra dehiscat, 
Our mare turgescat, pelago cur tantus amaror, 
Our caput obscura Phoebus ferrugine condat; 
Quid toties diros cogat flagrare cometas ; 
Quid pariat nubes, veniant cur fulmina coelo, 
Quo micet igne Iris, superos quis condat orbes 
Tarn vario motu." 

J, B, PineUi ad Mazonium. 




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CONTENTS OF VOL. V. 

(FIFTH SERIES). 



NUMBER XXVIIL— JANUARY 1878. 

P»g» 
Dr, 0. J. Lodge on a Form of Daniell Cell conyenient as a 

Standard of Electromotive Force. (Plate I.) I 

Sir W. Thomson on the Thermoelastic, Thermomagnetic, and 

Fyroelectric Properties of Matter 4 

Prof. J. Le Conte on Binocular Vision 27 

Profc H. F. Weber on Electromagnetic and Calorimetric Ab- 
solute Measurements : the Absolute Value of Siemens's Unit 
of Resistance in Electromagnetic Measure; the Relation 
between the Current-work and the Heat-evolution in sta- 
tionaiy GMvanic Currents;* and the Absolute Values of 
some constant Hjdroelectromotive Forces in Electromag- 
netic Measure 30 

Profs. W. B. Ayrton and J. Perrj on Ice as an Electrolyte. 

(PUte U.) 43 

Br. J. Croll on Le Sage's Theory of Qravitation 45 

MM. E. Fremy and Feil on the Artificial Production of Co- 
rundum, Ruby, and various Crystallized Silicates 47 

Mr. F. Field on a Variety of the Mineral Cronstedite 52 

Prof. Cayley on the Distribution of Electricity on two Sphe- 
rical Suifaoes 54 

Gaptain Abney on the Destruction of the Undeveloped Pho- 
tographic Image 61 

Notices respecting New Books : — 

Mr. H. F. Blanford's Report on the Administration of 
the Meteorological Department of India in 1875-76. 

Report on the Meteorology of India in 1875 63 

Lord Rayleigh's Theory of Sound 66 

Proceedings of the Royal Society : — 

Mr. W. Crookes on Repulsion resulting from Radiation. 
— ^Preliminary Note on the Otheoscope 68 



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IV CONTENTS OP VOL. V. — PIFTH SERIES. 

Page 

Proceedings of the Geological Society : — 

Mr. W. Shone on the GMacial Deposits of "West Cheshire, 
together with lists of the Fauna found in the Drift of 

Cheshire and adjoining Counties ' 72 

Mr. C. Lapworth on the Moffat Series 72 

On the Composition and Industrial Use of the G^ases issuing 

from Metallurgic Hearths, by L. Cailletet 75 

On a Pile in which the Attackable Electrode is of Coke, by 

P. JablochkofE 76 

On the Law of Absorption of Eadiations through Bodies, and 
its Employment in Quantitative Spectral Analysis (Part I.), 

by G. Govi 78 

Liquefaction of Oxygen 80 



NUMBEE XXIX.— FEBEUABT. 

Mr. J. Aitken on some Experiments on Eigidity produced by 

Centrifugal Force. (Plates HL-VII.) 81 

Prof. J. Emerson-Eeynolds on a New Form of Measuring- 
Apparatus for a Laboratory-Spectroscope 106 

Dr. 0. J. Lodge on a Method of measuring the Absolute 

Thermal Conductivity of Crystals and other rare Subsf»nces. 110 
Mr. S. T. Preston on the Application of the Kinetic Theory of 

Gases to Gravitation 117 

Prof. H. F. Weber on Electromagnetic and Calorimetric 
Absolute Measurements : the Absolute Value of Siemens's 
Unit of Eesistance in Electromagnetic Measure ; the Eela- 
tion between the Current-work and the Heat-evolution in 
stationary Galvanic Currents ; and the Absolute Values of 
some constant Hydroelectromotive Forces in Electromag- 
netic Measure 127 

Mr. W. J. Lewis's Crystallographic Notes 139 

Prof. J. Emerson-Eeynolds on the Eapid Estimation of Urea. 144 
Notices respecting New Books : — 

Dr. E. Frankland*s Experimental Eesearches in Pure, 

Applied, and Physical Chemistry 153 

Proceedings of the Geological Society : — 

The Eev. E. Abbay on the Building-up of the White 

Sinter Terraces of Eoto-M&b^n4, New Zealand 156 

Mr. H. Hicks on the Dimetian and Pebidian Bo'^ks of 

Pembrokeshire 157 

Three Experiments with Telephones, by Profesor E. Sacher . . 158 

On the Liquefaction of Hydrogen, by Eaoul Pictet 158 

On the Electrical Aftercurrents of transversely Magnetized 
Iron, by Professor H. Streintz 160 



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CONTENTS OF VOL. V. — FIPTH SERIES. V 

NUMBER XXX,— MARCH. 

Page 
Dr. J. Kerr on Reflection of Polarized light from the Equa- 
torial Surface of a Magnet 161 

Prof. J. J. Sylvester's Proof of the hitherto undemonstrated 

Pondamental Theorem of Invariants 178 

Prof. H. F. Weber on Electromagnetic and Calorimetric Abso- 
lute Measurements : the Absolute Value of Siem8ns*sUnit of 
^Resistance in Electromagnetic Measure; the Relation be- 
tvireen the Current-work and the Heat-evolution in stationary 
G-alvanic Currents ; and the Absolute Values of some con- 
stant Hydroelectromotive Forces in Electromagnetic Mea- 
sure 189 

Professors "W. E. Ayrton and J. Perry on Rain-Clouds and 

Atmospheric Electricity 197 

Mr. H. C. Russell on a new Modification of the Bichromate 

Battery (Plate VIII. fig. 14.) 201 

M. A. Ritter's Contributions to the Study of States of Aggre- 
gation. (Plate Vni. figs. 1-13.) 202 

Mr. W. H. Walenn on Unitation.— VIII. Practical Remarks 

thereon, together with Examples 214 

Professors W, E. Ayrton and J. Perry on the CJontact Theory 

of Voltaic Action '. 219 

Mr- T. Bayley on the Colour Relations of Copper and its Salts. 222 
Notices respecting New Books : — 

Mr. J. R. Capron's Photographed Spectra 225 

Mr. R. A. Proctor's Other Worlds than Ours 228 

Mr. E. J. Routh's Treatise on the Stability of a given 

State of Motion, particularly steady Motion 230 

Proceedings of the Geological Society : — 

Mr. H. Hicks on some Precambrian (Dimetian and Pebi- 

dian) Rocks in Caernarvonshire 231 

Prof. T. M*Kenny Hughes on the Precambrian Rocks of 

Bangor 232 

Mr. W. A. E. IJssher on the Chronological Value of the 

Pleistocene Deposits of Devon 233 

Dr. C. Le Neve Foster on the Great Flat Lode south of 
Redruth and Camborne ; and on some Tin-mines in the 

Parish of Wendron, Cornwall 234 

Dr. C. Le Neve Foster on some of the Stockworks of 

Cornwall 235 

The Eevs. E. Hill and T. G. Bonney on the Precarboni- 

ferous Rocks of Chamwood Forest 236 

'On some Measurements of the Polarization of the Light coming 
from the Moon and from the Planet Venus, by the Earl of 

Rosse, F.R.S 237 

Glass-engraving by Electricity, by M. Plante 238 

On the Photometric Comparison of Light of different Colours, 
by Professor O. N. Rood, of Columbia College, U. S. A. . . 239 



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VI CONTENTS OF VOL. V, — FIFTH SERIES. 

NTJMBEB XXXI.— APEIL. 

Page 

Professors W. E. Ajrrton and J. Perry on the Heat-conduc- 
tivity of Stone, based on Fourier's Theorie de la Chaleur. 

(Plates IX. & X.) 241 

Sir Gt, B. Airy on the Correction of the Compass in Iron Ships 

without use of a Fixed Mark. (Plate XI.) 267 

Mr. S. P. Thompson on Permanent Plateau's Films 269 

Mr. H. F. Morley on Grove's Gas-Battery 272 

Mr. W. H. Preece on some Physical Points connected with the 

Telephone 281 

Prof. P. E. Chase on the Nebular Hypothesis.— VII. Undula- 
tion 292 

Mr. S. T. Preston on the Bearing of the Kinetic Theory of 
Gravitation on the Phenomena of " Cohesion " and " Che- 
mical Action/' together with the important connected In- 
ferences regarding the existenceof Storesof Motion in Space. 297 
Notices respecting New Books : — 

Des Paratonnerres k Pointes, k Conducteurs et k Eac- 
cordements Terrestres Multiples. Description detaill^e 
des Paratonnerres etablis sur I'Hotel de Ville de 
Bruxelles en 1865. Expose des Motifs des disposi- 
tions adopt^s par Melbbns, Membre de I'Acad. Eoy. 

de Belgique 311 

Proceedings of the Geological Society : — 

Prof. J. W. Judd on the Secondary Bocks of Scotland . . 313 
On Galvanic Currents between Solutions of dijfferent degrees 
of Concentration of the same Substance, and their Series of 

Tensions, by Dr. James Moser 317 

On the Extraction of GbtUium, by MM. Lecoq de Boisbaudran 

and E. Jungfleisch 318 

On the Resistance of Fluids 320 



NXJMBEE XXXn.— MAT. 

Prof. G. Quincke on the Edge-angle and Spread of Liquids on 

Solid Bodies. (Plate Xn.) 321 

G. W. von Tunzelmann on the Production of Thermoelectric 

Currents in Wires subjected to Mechanical Strain 339 

Prof. Helmholtz on Galvanic Currents occasioned by Differ- 
ences of Concentration — ^Inferences from the Mechanical 

Theory of Heat 348 

Mr. R. MaUet on the Eate of Earthquake- wave Transit .... 358 
Prof. P. E. Chase on the Nebular Hypothesis.— VIII. Criteria. 362 
Prof. B. B. Clifton on the Difference of Potential produced 
by the Contact of different Substances 367 



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CONTENTS Of VOL. V. — FIFTH SERIES. Vll 

Plge 

Sir W. Thomson on Problems relating to Underground Tem- 
perature. A Fragment 370 

Dr. L. Bleekrode on the Electric Condactiyit j and Electrolysis 

of Chemical Compounds 375 

Notices respecting New Books : — 

Die Potenti^function und das Potential, ein Beitrag zur 

mathematischen Phjsik von B. Clausius 889 

Proceedings of the G^logical Society : — 

Mr. A. B. Wynne on the Physical Geology of the Upper 

Tnnyib 392 

Mr. J. S. Gardner's Description and Correlation of the 

Bournemouth Beds 393 

Mr. B. Daintree on certain Modes of Occurrence of Gold 

in Australia 394 

Mr. W. H. T. Power on the Geology of the Island of 

Mauritius and the adjacent Islets 394 

On the Pitch of a Tuning-fork in an Incompressible Fluid, by 

Felix Auerbach 395 

A Note on Experiments with Floating Magnets ; showing the 
Motions and Arrangements in a Plane of freely moyinff 
Bodies acted on by Forces of Attraction and Eepulsion, and 
serriug in the Study of the Directions and Motions of the 

lines of Magnetic Force, by Alfred M. Mayer 397 

On Sensations of Light and of Colour, in Direct and Indirect 

Vision, by E. Landolt and A. Charpentier 398 

On the Galvanic Polarization of Platinum in Water, by Dr. 
F. Exner 400 



NUMBEE XXXIII.— JUNE. 

Mr. E. Sabine on some Electrical Experiments with Crystalline 
Selenium 401 

Prof. G. Quincke on the Edge-angle and Spread of Liquids on 
Solid Bodies 415 

Mr. F. Guthrie on the Influence of Temperature on the Pas- 
sage of Air through Capillary Tubes 433 

Dr. L. Bleekrode on the Electric Conductivity and Electrolysis 
of Chemical Compounds 439 

Prof. Challis's Theoretical Explanations of the Actions of the 
Badiometer, the Otheoscope, and the Telephone 452, 

Mr. G. J. Stoney on some remarkable Instances of Crookes's 
Layers, or Compressed Strata of Polarized Gas, at ordinary 
Atmospheric Tensions 457 

Messrs. .1. A. Wanklyn and W. J. Cooper on Water-Analysis. 
Determination of Cellulose and modified Cellulose in Drink- 
ing-Water 464 



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via CONTENTS OF VOL. V. — FIFTH SERIES. 

Page 
Notices respecting New Books ; — 

Prof. S. Newcomb*8 Popular Astronomy 467 

Capt, W. de W. Abney's Treatise on Photography, and In- 
struction in Photography 469 

Proceedings of the Geological Society : — 

Prof. A. C. Bamsay on the Geology of Gibraltar 471 

Mr. J. G. H. Godfrey on the Qedogy of Japan 473 

Contribution to the Theory of the Motion of Electricity in Sub- 
marine and Underground Telegraph-wires, by G. Kirchhoff . 474 
Experiment for Illustrating the Terrestrial Electrical Currents, 

by Professor W. Leroy Broun 475 

On the Diffusion of Carbonic Add through Water and Alcohol, 
by Professor Stefan 476 



PLATES. 

I. lUustratiye of Dr. O. J. Lodge's Paper on a Form of Daniell Cell 
conyenient as a Standard of Electromotive Force. 

n. Illustrative of Professors Ayrton and Perry's Paper on Ice as an 
Electrolyte. 

m.-VU. niustrative of Mr. J. Aitken's Paper on Bigidity produced by 
Centrifugal Force. 

Vm. Illustrative of A. Bitter's Paper on States of Aggregation; and Mr. 
H. C. Bussell's on anew Modification of the Bichromate Battery. 

IX., X. Illustrative of Professors Ayrton and Perry's Experiments on the 
Heat-conductivity of Stone. 

XL niustrative of Sir G. B. Aiiy's Paper on the Correction of the 
Compass in Iron Ships. 

XII. Illustrative of Prof. G. Quincke's Paper on the Edge-angle and 
Spread of Liquids on Solid Bodies. 



EBBATUM IN VOL. IV. 
Page 461, lines 16-21,/or P^ read P. 

EBBATA IN VOL. V. 

In footnote, page 206, for Pliicker read Biicker. 

Page 216, lines 3 and 4, /or 

7 4 5 I : 6 2 5 
«a fla «i • ^o' ■ <»-I <*-« <*-3 

read 7 4 6 i • : 6 2 6 

«a flj ^i I Oq \ a-i a»2 a. 5^ 



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/ 






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?Vi]l.Mag.S,5.Vbl.5,PVi. 



Fig. 2. 



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THE 
LONDON, EDINBURGH, and DUBLIN 

PHILOSOPHICAL MAGAZINE 

AND 

JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



/ 



/,■ 



JAir U AB Y 187S. ^ /Cr'>, 

I. On a Form of Daniell Cell convenient as a Standard of Elec- 
tromotive Force. By Ouveb J. LoDGE^ D.Sc,* 

[Plate L] 

ALTHOUGH a volt is the formal unit of electromotive 
force^ yet it happens in practice that diiFerences of po- 
tential get stated as equal to so many Daniell cells more fre- 
qiiently than any thing else^ showing that there is some decided 
convenience in this mode of statement, a convenience partly 
owing, no doubt, to the fact that a freshly set-up Daniell is a 
tolerably uniform and easily reproduced standard. An ordi- 
nary Daniell, however, is by no means suitable as a standard, 
because of the diffusion of the copper-liquid through the porous 
celL This defect must obtain in any cell where two liquids 
separated by a porous partition are employed ; and hence 
attempts have bc«n made to construct standard cells with solid 
electrolytes, or with mercury instead of copper salts, as in the 
litde cell devised by Mr. Latimer Clark, which, though not 
absolutely constant, is still, I suppose, the best for its special 
purpose. But all ceUs with solid electrolytes are extremely 
inconstant, in the sense that they suffer greatly from short- 
circuiting and take some time to recover themselves; and 
there are some other inconveniences attending the use of a 
large number of Clark's cells. 

A convenient Daniell Cell with high internal Resistance. 

Of all known cells, a Daniell charged with sulphate of zinc 
and sulphate of copper seems to be the most perfect — in this 

• Communicated by the FhTsical Society — one of the ceUs having 
been exhibited at a meeting of the Society in February 1877. 
Pha. Mag. S. 5. Vol- 5. No. 28. Jan. 1878. B 

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2 Dr. 0. J. Lodge on a Fonn of Daniell Cell 

respect, that the materials remain always the same daring 
action except that the 'Sulphate of zinc gradually increases in 
quantity, a difference which scarcely affects the electromotive 
force. Almost the only defect in the constancy of a oell so 
charged is due to the fact that the two liquids diffuse into 
each other, for which reason the battery cannot retain its 
original state after it has stood for some time. Any thing 
equivalent to a porous partition is quite useless for keeping the 
liquids separate ; and the only plan seems to be to provide as 
long a column of liquid as possible for the copper salt to dif- 
fuse through. 

This is done in a compact and simple manner in the cell 
represented in fig. 1 (PI. L). A wide-mouthed bottle (or a tall 
jar) is fitted with a cork through which passes a wide glass tube 
open at both ends. To the lower end of this tube a short 
closed tube (like a test-tube) is tied with silk thread ; a long 
strip of sheet zinc is put down the open tube ; and a copper 
wire, recurved at the bottom and coated with sealing-wax ex- 
cept at its two ends, is passed through the cork to t£e bottom 
of the closed tube, where it is imbedded in a few crystals of 
copper sulphate. The bottle is then nearly filled with dilute snl- 

Ehate of zinc, and the cork with the tube is inserted, the latter 
eing so arranged that the end of the zinc strip and the mouth 
of the short tube are both below the surface of the liquid. In 
a short time a strohg solution of sulphate of copper forms at 
the bottom of the closed tube where the copper wire is bare, 
and it gradually diffuses upward ; but in order to reach the 
zinc it has to diffuse itself all through the water of the bottle 
and then up the long tube containing the zinc ; and this takes 
a long time, though it certainly does take place to some extent 
in a week or so. 

But when I want to put the cell by for any length of time, 
I pull the long tube a little higher up through the cork, so 
that the moutn of the short tube emerges above the liquid and 
thus entirely prevents diffusion. The zinc strip is also raised 
out of the liquid by the same action. It is convenient to have 
the cork fitting pretty air-tight ; or else evaporation may go 
on from the edges of tfie tube, and the salts which crystallize 
there may continue the diffusion slowly. 

The copper wire need not be covered with wax or anything ; 
but if it were not, its upper parts would assist in the action 
until they were polarized ; and hence the interaal resistance 
would be liable to vary, which is not desirable. The internal 
resistance of such a cell is always rather high : for instance, 
in the one of which fig. 1 is a portrait, the bottle stands about 
6 inches high, and the internal resistance is about 500 obma 



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as a Standard of Electromotive Force. 3 

whan arraaged as shown ; bafc of conrse it depends greatly on 
the position of the tabes^ and also somewhat on the tempera^ 
tare. Hence it is not to be regarded as giving necessarily a 
Teiy constant current^ but rather as a ceil which can be used 
for a long time and yet keep its electromotive force nearly un« 
changed. 

I have also made a set of small cells on the same principlci 
with ordinary quilled tubing for the tubes, and with test-tubes 
for the containing vessels, making the connexions by twisting 
the thin copper wire of one cell round the projecting tube 
(with \he zinc bent down springily over it) of the next. A 
large number of such cells may be quickly made and ari*anged 
in ordinary test-tube stands; and they are convenient for 
many purposes, such as capacity- or insulation-testing, where 
high electromotive force is required*. The whole rack of 
oells was once accidentally upset ; but though a little liquid 
escaped from the open ends of the zinc-tubes, the copper-liquid 
remained steady at the bottom of its tube without visible dis- 
turbance. 

A Cell for a Standard of Electromotive Force, 
Fig. 2 shows a bottle about 3 inches high, which I have 
made to act as a standaixl of electromotive force. It differs in 
DO essential respect from fig. 1, except that the mouth of the 
tube containing the copper-solution never dips below the sur- 
face of the liquid, but always projects J inch above it. The 
other or open tube does not project at all above the cork ; and 
its lower end is drawn oTit and coiled round so as still further 
to retard the passage of the copper-liquid to the zinc. The 
zinc, which should be pure, is supported at the right height 
by a pin thrust through it. The closed tube is proportionally 
longer than in fig. 1 ; it is nearly filled with pure sulphate-of- 
copper solution, a few crystals being placed at the bottom ; 
and it is tied to the other tube, as before, with silk thread 
(which appears not to rot). The copper wire is gutta-percha^ 
covered with its ends bared. The bottle is filled nearly to its 
neck with very dilute sulphate of zinc ; and the cork is then 
inserted air-tight. 

No mixing of the liquids is now possible ; but conduction 
still takes place over the damp surface of the glass tube, espe- 
cially if, before use, the whole bottle be slightly inclined so as 
to wet tibe edges of the tube. The slight film of zinc-salt thus 
formed, being hygroscopic and being in a saturated atmo- 

* I suppose that by ufiing platinum instead of copper wire, and strong 
idlric acia or else sulphuric acid and bichromate of potash instead of the 
copper salt, one could nearly double the electromotive force, though with 
•Qme loss of constancy. 

B2 

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4 Sir W. Thomson on the T/iemwelasticy Thennomagneticy 

sphere, will keep the top of the tabe safficiently moist for an 
immoDse time. 

The only possible changes which can go on in this cell are 
in the zinc and the solution in immeaiate contact with it. 
This solution can at any time be drawn pflF with a pipette and 
replaced by fresh, without greatly affecting the liquid in the 
bottle (if the cork be air-tight) ; and the zinc can still more 
easily be taken out and replaced by a new piece. 

I have described the cell as at present made ; but if there 
were any chance of its coming into use as a standard, a few 
modifications might be introduced. Thus the zinc might be 
a short rod with an india-rubber collar fitting the tube and 
with a short copper wire attached to it, which should project 
above the cork instead of the zinc, the joint being a little way 
down the tube and protected by a coat of varnish from damp 
air. A set of experiments would have to be made to determine 
the dependence of electromotive force on temperature ; and 
then a thermometer with a short scale might be fixed in each 
cork. 

UniTersity College, London. 



IJ. Cr the Thermoelasticy Thermomagneticj and Pyroelectrie 
Prcperties of Matter. By William Thomson, M.A.y l^xte 
Fellow of St. Peter* s College, Cambridge^ Professor of Nor- 
t%.ral Philosophy in the University of Glasgow*. 

1. A BODY which is either emitting heat, or altering its 

-J^ dimensions against resisting forces, is doing work upon 

matter external to it. The mechanical effect of this work in 

* [This ]japer is in the main a reprint from an article which appeared 
under the title " On the Thermoelastic and Thermomagnetic Properties 
of Matter, Part I.," in April 1856, in the first nuniher of the ' Quarterly 
Journal of Mathtmatics/ but which waa confinnl to the thermoelastic 
part of the subject. The continuation, in which it was intended to 
make a similar application of thermodynamic principles to magnetic in- 
duction, waa never published or written ; but the results which it should 
have contained were sufficiently indicated in a short ai tide on ^^ Thermo- 
magnetism," which I wrote at the request of my friend and colleague the 
late Professor J. P. Nichol for the second edition of his • Cyclopiedia,' 
published in 1860, and which I include in the present reprint. The 
addition of " Pyro-Electricity," which I now mate to the title of the 
former article, is justified by another short quotation from the second 
edition of Nicholas 'Cyclopfiedia' (article " Thermo-Electridty, Divi- 
sion L—Pyro-Electricity, or Thermo-Electricity of Nonconducting Crys- 
tals "), and a short addition, now written and published for the first time, 
in which the same thermodynamic principles are applied to this form of 
thermoelectric action. 

Several additions both in the shape of text and footnote are appended 
in the course of the reprint. These are all distinguished by being en- 
closed in brackets^ [ ].] 



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imd Pyrodedric Properties of Matter. 5 

one case is ihe excitation of thermal motions, and in the other 
the OYercoming of resistances. The body most itself be alter* 
ioj^ in its circumstances, so as to contain a less store of energy 
within it, by an amonnt precisely eqnal to the aggregate yalue 
of the mechanical effects produced ; and conversely, the ag- 
grefi[ate Talne of the mechanical effects prodaced must depend 
solely on the initial and final states of the body, and is there- 
fore the same, whatever be the intermediate states through 
which the body passes, provided the initial andjinal states be 
the same* 

2. The total intrinme energy of a body might be defined as 
the mechanical value of all the effect it would produce, in heat 
emitted and in resistances overcome, if it were cooled to the 
utmost, and allowed to contract indefinitely or to expand inde- 
finitely according as the forces between its particles are attrac- 
tive or repulsive, when the thermal motions within it are all 
stopped ; but in our present state of ignorance regarding per- 
fect cold, and the nature of molecular forces, we cannot deter- 
mine this " total intrinsic energy'' for any portion of matter ; 
nor even can we be sure that it is not infinitely great for a 
finite portion of matter. Hence it is convenient to choose a 
certain state as standard for the body under consideration, and 
to nse the unqualified term intrinsic energy with reference to 
this standard state ; so that the '^ intrinsic energy of a body in 
a given state " will denote the mechanical value of the effects 
the body would produce in passing from the state in which it 
is given, to the standard state — or, which is the same, the me- 
chanical value of the whole agency that would be required to 
bring the body from the standard state to the state in which it 
is ^ven. 

3. In Part V.* of a series of papers on the Dynamical Theory 
of Heat, communicated to the Boyal Society of Edinburgh, 
a system of fermulsB founded on propositions established in 
Part I.t of the same series of papers, and expressing, for a 
given fluid mass, relations between its pressure, its thermal 
capacities, its intrinsic energy (all considered as functions of 
its temperature and volume), and Camot's function of the 
temperature, were brought forward for the purpose of pointing 
out the importance of making the intrinsic energy of a fluid in 
different states an object of research along with the other 
elements' which have hitherto been considered, and partially 
investigated in some cases. In the present communication a 
similar mode of treatment, extended to include solid bodies. 
nnmagnetic [and unelectrified], or magnetized [or electrified J 

• Trans. Roy. Soc Edinb. December 16, 1851. 
t Ibid. March 17, 1851. 



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6 SirW. Thomson on the Thermoelastic, Thermomagnetic, 

in any way, is shown to lead to the most general possible 
theory of elasticity, whether of solids or fluids, and to point 
out various thermodynamic properties of solids and various 
thermal effects of magnetism [and of electricity] not hitherto 
discovered. 

Section I. — Elasticity of Solids or Fluids not subjected to 
Magnetic Force. 

4. Let Xj y, z^ f , 17, 5 be six independent variables expressing 
the mechanical condition of a homogeneous solid ma^s, ho- 
mogeneously strained in any way*, and let ^ be its tempe- 
rature ; and (in accordance with the preceding explanations) 
let e denote its intrinsic energy, reckoned from a certain 
"standard state" defined by particular values, Xq, Voy *oj 
f oj Voj Soj ^0? on which its physical condition depends. Thus, if 
^ denotes a certain function depending on the nature of the 
substance, and vanishing for the values Xq, yoj • • • *o of ^e inde- 
pendent variables, we have 

tf=^(^,y,2:, f, 17, f, 0; . . . . (1) 
and a knowledge of the function <f> [with besides a knowledge 
of w for one particular temperature f] comprehends all the 
thermoelastic qualities of the solid. 

5. Now let us suppose the body to be strained so as to pass 
from the mechanical state (^o? yo? ^ot (oy Voy So) ^o (^j !/) ^y f ? Vy 5) 
while it is constantly kept at the t<mipeniture t ; and lot H de- 
note the quantity of heat that must be supplied to it during 
this process to prevent its temperature from being lowered (a 
quantity which of course is zero, or negative, for such strains 
as cause no thermal effects, or which cause positive evolutions 
of heat). Let the body be brought back to its mechanical con- 
dition (xq, yo, Zq, fo> Voy So) through the same or any other of 
all the infinitely varied successions of states by which it may 
be made to pass from one to the other of the two which have 
been named, its temperature being kept always at t. Then, 
by the second Fundamental Law of the Dynamical Theory of 
Heat (see Trans. Boy. Soc. Edinb. May 1, 1854, p. 126), we 
must have tt ti' 

and therefore H'a=:— H. 

* The terms a drain, or to drain, are used simply with reference to 
alterations of dimensions or form in a solid — the forces bj which ''a 
strain" is produced bein^ called the straining tensioM or pressureSj or 
sometimes merely the tensions or pressures, to which the solid is subjected. 
This distinction of terms is adopted in accordance with the expressions 
used by Mr. Rankioe in his paper on the Elasticity of Solids (Cambridge 
and Dublin Mathematical Journal, February 1861). 

t [See equations (10), (11) of § 7 below.] 

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and Pyroelectric Properties of Matter. 7 

6. We condnde that the quantity of heat absorbed by the 
bodj in being strained from one state to another at the same 
temperatore is quite independent of the particular succession of 
states through which it is made to pass, provided it has through- 
oat the same temperature. Hence we must have 

H=f(^, y, z, f , V, ?, 0-^(^0, yo, zo, fo, Vo, 5), 0> • (2) 

where -^ denotes a function of the variables. Now the me- 
chanical value of the heat taken in by the body while it passes 
trom one condition to the other, together with the work spent 
in compelling it to do so, constitutes the whole augmentation 
of mechanical energy which it experiences ; so that if e denote 
this augmentation — that is, if 

^=K^7 yy ^j ?? 'ny ?, O--0('^o, yo, ^o, foj %; &? 0^ • (3) 

and if w denote the work done by the applied forces and J the 
mechanical equivalent of the thermal unit, we have 

€=tr+JH (4) 

From this we conclude that the work required to strain the 
body from one to another of two given mechanical states, 
keeping it always at the same temperature, is independent of 
the particular succession of mechanical states through which 
it if' made to pass, and is always the same when the initial and 
final states are the same. Tms theorem was, I believe^ first 
given by Green (as a consequence of the most general con- 
ceivable hypothesis that could be framed to explain the mutual 
actions of the different parts of a body on which its elasticity 
depends), who inferred from it that there cannot be 36, but only 
21, independent coefficients [or "moduluses "] of elasticity, with 
reference to axes chosen arbitrarily in any solid whatever. It 
is now demonstrated as a particular consequence of the Second 
General Thermodynamic Law. It might at first sight be re- 
garded as simply a consequence of the general principle of 
medianical effect ; but this would be a mistake, fallen into 
from forgetting that heat is in general evolved or absorbed 
when a solid is strained in any way ; and the only absurdity 
to which a denial of the proposition could lead would be the 
possibility of a self-acting machine going on continually draw- 
ing heat from a body surrounded by others at a higher tem- 
perature, without the assistance of anv at a lower temperature, 
and performing an equivalent of mecnanical work. 

7. The full expression of the Second Thermodynamic Law for 
the circamstances of elastic force is, as is shown in the pas- 
sage referred to above (Trans. Roy. Soc. Edinb. May 1, 1854, 
p. 126), that if H/, H'/, &c. denote the quantities of heat emitted 



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6 SirW. Thomson on the Thermoelastic, T/ierniomaffnetic, 

from a body when at temperatures* f, ^ respectively, during 
operations changing its physical state in any way, the «um 

2 -y must vanish for any cycle of changes, if each is of a per- 
fectly reversible character, and if at the end of all the body 
is brought back to its primitive state in every respect. Let 
us consider, for instance, the following cycle, which obviously 
fulfils both conditions. 

(I.) Let the body, initially in the state (^Tq, y^, zq, fo> Voi £)j 0> 
be raised in temperature from ^ to ^, its form and dimensions 
being maintained constant, 

(11.) Let it be strained from the state (^o> yoj ^Of fo> Voj &) 
to the state (ar, y, z, f , 97, f), while its temperature is kept 
always at f, 

(III.) Let it be lowered in temperature from ^ to ^, its form 
and dimensions bsing retained. 

(IV.) Let it be brought back to the mechanical state 
(^oj yo> ^oj fo> Vof So)^ while its temperature is kept constantly 
at t. 

The quantities of heat taken in by the body in these succes- 
sive operations are respectively : — 

(I-) ji^i^o, !/o, ^Oj foj ^0; Si), O ""^(-^Oj yoj ^oj foj V07 So? t)}, 

because the difference, of the whole mechanical energies is 
simply the mechanical value of the heat taken in or emitted in 
all cases in which no work is either done on the body or re- 
ceived by it in virtue of the action of applied forces ; 

(IL) ylr(x, y, z, f, rj, f, O-'^C^o, !/o, z^, fo, ^0, 5), ^), 
according to the notation expressed by equation (2) above ; 

(III-) - J {4>{^y yy h f; ^; ?, t')-^{x, y, z, f, 17, f, f)}, 

and 

(IV.) -{i/r(^,y, z, f,^,5,0-'^(^o,yo,^o,fo,%,?ro, 0}- 

• Reckoned on the absolute thermodynamic scale, according to which 
" temperature *' is defined as the mechanical equivalent of the thermal unit 
divided by " Carnot's function." In a paper " On the Thermal Effects d 
Fluids in Motion/' by Mr. Joule and myself, communicated to the Royal 
Society last June [ 1854], and since published in the Philosophical Transac- 
tions, it is shown that temperature on the absolute thermodynamic scaledoes 
not aififer sensibly from temperature on the ordinary scale of the air-ther- 
mometer, except by the adclition of a constant number, which we find \a 
be about 2737 for the Centigrade scale. Thus, on the system now adopted, 
the temperature of melting ice is 273-7, that of boilmg water is 3737, 
and differences of temperature are sensibly the same as on an ordioarjr 
standard Centigrade thermometer. 



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and Pyroelectric Properties of Matter. 9 

If we suppose ^— * to be infinitely small, these expressions be- 
come respectively, in accordance with the previous notation: — 

(I) ^^(^-0, 

where eo denotes the valne of e for (xqj yoj ^o^ f o, Vj £)> 5 
(n.) H + ^(C-(); 



v.. '^ 



(IV.) -H. / 

Hence we Iiave /- , '/• -/ , 

or, since «— <'o is what we have denoted by e, 

and die expression of the Second Thermodynamic Law becomes 



<f) : 



EUminating € from this by (4), we have 

^—\% w 

and, eliminating H, 

"-'% 0) 

This is eqaivalent to 

e^e^-\"w—t-^-\ (8) 

or, if No denote this specific heat of the mass at any tempera- 
ture iy when kept constantly in the mechanical state (op^jyo, ^oy 



e 



=jf Narf< + u;-<~, .... (9) 

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H 



10 Sir W. Thomson on the Tliermoelasticy ThermomagnetiCj 

an eicpression which shows how the " intrinsic energy " of the 
•body may be determined from observations giving ti? as a 
function of the seven independent variables, and Nq as a func- 
tion of the temperature, for a particular set of values of the 
geometrical elements. Conversely, by (5) we have 

=jj^-^'' (10) 

and by (6) and (7), or simply by (4), 

«7=€-JH; (11) 

which show how H and w may be determined for all tempera- 
tures from a knowledge of the intrinsic energy of the body, 
and of [one of] those functions themselves for a particular tem- 
perature. 

8. Let K denote the specific heat of the body at any tempe- 
rature tj when it is allowed or compelled to vary in form and 
dimensions with the temperature, according to any fixed law — 
that is, when each of the variables Xj y, Zy f , 97, f is a given 
function of t ; and let N denote what this becomes in the par- 
ticular case of each of these elements being maintained at a 
constant value ; or, which is the same, let N be the specific 
heat of the body at any temperature when maintained at con- 
stant dimensions {x, y, r, f , 97, f). We have 

JN=| (12) 

g._ de </(JH) dx rf(JH) ^ <f(JH) cfe 
~ dt dx dt dy dt dz dt 

^ d^ dt^ dv dt^ d^ dt' ' ^^"^^ 

Since JH is equal io e—w, this expression may be modified 
as follows : — If D denote the total difterential of e, 
j-^ __ J)e (dw dx dw dy dw dz 
"" dt \dx dt dy dt dz dt 

dwd^ dw dv , dw d^ n^j^-x 

^diTt^d^Tt-^-T^dty • • ^^^^^ 

9. These equations may be applied to any kind of matter ; and 
they express all the information that can be derived, from the 
general thermodynamic principles, regarding the relations be- 
tween thermal and mechanical effects produced by condensa- 
tions, rarefactions, or distortions of any kind. For the case of 
a fluid they become reduced at once to the forms investigated 
specially for fluids in my previous communications. Thus, if 
the mass considered be one pound of any kind of fluid, we may 



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and Pyroelectrie Properties of Matter. 1 1 

lake one of the six variables ^, y, z, 0, 17^ (^ as the volume t?, 
which it is made to occupy in any particular condition, and the 
remaining five will not affect its physical properties, and will 
therefore disappear fronr all the preceding equations ; and the 
state of the fluid will be completely defined by the values of 
the two independent variables v, t. Then, if p denote the pres- 
sure, we must have 

dw 

since —pdv is the work done upon a fluid in compressing it 
nnder pressure p from a volume w to a volume v H- dv, JBut 
from (9) we have 

and, therefore, 

and 



de ^ dw d dw 
dv "^ dv dt dv 



t-'i-p <") 



■^-'1- (»«•) 

Hence (13) becomes 

where ( ^-) expresses the assumed relation between the natu- 
rally independent variables t?, t. If this be such that the pres- 
sure is constant, we have 

dp 
dv dt 
dt'^ _dp' 
dv 

and, K being now the specific heat under constant pressure, we 
have finally 

^-t-^ 0^) 

dv 

10. These equations (14) and (15), together with the unmo- 
dified equation (12), which retains the same form in all cases, 
express the general thermodynamic relations between the 
intrinsic energy, the pressure, and the specific heats of a fluid. 
If we eliminate €, we have 



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12 SirW. Thomson on tlie Thermoelastic, Tliermomagneticj 

• JK-JN=-1^ . . . , (16) 

dv 
and rf(JN)_^ 

which are the eqaations used to express those relations in a 
recent paper by Mr. Joule and myself, " On the Thermal 
Effects of Fluids in Motion " *. 

If, instead of — --, we substitute fidt, considering fi as a 
t 

function of Camot's function of the temperature, they be- 
come identical with the two fundamental equations (14) and 
(16) given in Part III. of my first communication " On the 
Dynamical Theory of Heat" t- 

11. To apply tne preceding equations to a body possessing 
rigidity, it is necessary to take the form as well as the bulk into 
account, and therefore to retain, besides the temperature, six 
independent variables to express those elements. There is, of 
course, an infinite variety of ways in which the form and bulk 
of a homogeneously strained body may be expressed by means 
of six independent variables. Thus the lengths (three vari- 
ables) and the mutual inclinations (three variables) of the 
edges of a parallelepiped enclosing always the same portion of 
the solid in all states of strain (which of course always remains 
a parallelepiped, provided the strain is homogeneous through- 
out the solid), may be chosen for the independent variables ; 
or we may choose the six elements of an ellipsoid enclosing 
always the same portion of the solid (which will always remain 
an ellipsoid however the solid be strained, provided it is strained 
homogeneously. Thus, let us actually take for a, y, z the lengths 
of three conterminous edges OX, OY, OZ of a certain paral- 
lelepiped of the solid, and for f , 97, f the angles between the 
planes meeting in these edges respectively, the parallelepiped 
being so chosen that it becomes strained into a cube of unit 
dimensions, when the solid is in the particular state at which 
we wish to investigate its thermoelastic properties. 

12. If then we take 

^0=1? yo=i> ^0=1? 

fo=i'"", ^o=i'"", fo=j7r, 
and if we suppose a, y, z, f , 17, f to differ infinitely little from 
^0; yo, zo, f 0, 97p, ^ respectively, the actual state ( j?, y, z, f , 17, f) 
will be one m which the body is strained from the state 

* Transactions of the Royal Society, June 15, 1854. 

t Transactions of the Rojal Society of £dinbuigh, March 17, 1851. 

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and PyroeUdric Properties of Matter, 13 

(*ojyoj ^Qj ?o> %> ?o) ^y ^® edges of the cube being elongated by 
«— j?Q, y — y^, 2^— -?oj *^^ ^® angles meeting in three contermi- 
nous edges receiving augmentations of ^— fo, 17—%, ?— ?o' 
It is clear, since the altered angles differ each infinitely little 
from a right angle, that the strains represented by f— foj 
ij— i/o, f — 5) ii^volve no change of volume, and are simple de- 
formations, each of a perfectly definite kind, in the planes 
YOZ, ZOX, XOY respectively, and that the change of vo- 
lume due to the six coexistent strains is actually an infinitely 
small augmentation amounting to 

13. Considering still x—x^ &c. as each very small, we have 
the following development by Maclaurin's theorem, the zero 
suffixes to the differential coefficients being used for brevity to 
denote the values of the difierent coefficients at (x^^ y^, z^^ 
foj %i Si)- 

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14 Sir W. Thomson on tJie Thermoelaaticy Thermomagneticj 

14. According to the system of yariables * which we have 
adopted, as set forth in § 12, when x-^x^ &c. ire each infinitely 
small, X increasing corresponds to a motion of all the particles 
in a plane at a distance unity from YOZ, in directions perpen- 
dicular to this plane, througli a space numerically equal to the 
increment of ^ ; | increasing corresponds to a motion of all the 
particles at a distance unity from XO Y, in directions parallel to 
YO, through a space equal to the increment of f, or to a motion 
of all the particles at a distance unity from XOZ, in directions 
parallel to ZO, through a space equal to the increment of f , or 
to two such motions superimposed, through any spaces respec- 
tively, amounting together to a quantity equal to the incre- 
ment of f . Similar statements apply to the effects of variations 
of the other four variables. Hence, if P, Q, R denote the nor- 
mal components of the superficial tensions experienced respec5- 
tively by the three pairs of opposite faces of the unit cube of 
the solia in the state of strain in which we are considering it, 
and if S, T,' U be the components, along the planes of the faces, 
of the actual tensions, taken in order of symmetry, so that S 
denotes the component, perpendicular to the edge opposite to 
OX, of the superficial tension in either of the faces meeting in 
that edge (winch are equal for these two faces, or else the cube 
would not be in equilibrium, but would experience the effect 
of a couple in a plane perpendicular to OX), and T and U de- 
note components, perpendicular respectively to OY and OZ, 
of the superficial tensions of the pairs of faces meeting in those 
edges, the work done on tlie parallelepiped during an infi- 
nitely small strain in which the variables become augmented 
by dxy dy, &c. respectively will be 

PAc + Qrfy + IW^ + SJf + TdT; + UJf. 

Hence, if the portion of matter of which the intrinsic energy 
is denoted by ^, and to which the notation e, u', &a applies, be 
the matter within the parallelepiped referred to, we have 

5^-^' ^-«' ^-"' I . 

15. Using the development of to expressed by (1 8), we derive 
from these equations the following expressions for the six 
component tensions : — 

* [A method of generalized stress and strain components is fully de- 
veloped in "Elements of a Mathematical Theoiy of Elasticity," first pub- 
lished in the Transactions of the Royal Society for Apm 1856, and 
embodied in an article on "Elasticity," about to be published in the 
Encyclopadia Britannica.'] 



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and Ft/roelecttnc Properties of Matter, 15 

M^l«-«-G^).<'-'.)-(^t).«-»' J 
^G^).(»-'.)-(li).(^-^.)^(|£).('-'.) 



+ 



(f).<f-f«)H^>-*)^(||)«-W' 



\dr}/Q 



(21) 



^G^>-'^)-GlT>-^»)^(a-).(--) 
*G^).('--)-G^).(^-.)-(^).(^-) 

H^Vf-a^G^lc-'.)-©. (f-w. J 

16. These equations express in the most general possible man- 

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16 Sir W. Thomson on the Thermoelcuticj T/iermotnoffnetie, 

ner the conditions of equilibrium of a solid in any state of strain 
whatever at a constant temperature. They show how the 
straining forces are altered with any infinitely small alteration 
of the strain. If we denote bv Pq &c. the values of P Ac. for 
the state (xq, f/Q, Zq, foj Vo, So? t), the values of P— Pq, Q— Qo, 
R— Bo, S— So, T— -To, U— Uo given by these equations as 
linear functions of the strains (^— a?o)>(y— yo)> (-2^— ^)j (f —foL 
(^— q^)^ (J^— 5j)j with twenty-one coefficients, express the whole 
tensions required to apply these strains to the cube, if the con- 
dition of the solid when the parallelepiped is exactly cubical 
is a condition of no strain^ and in this case become (if single 

letters are substituted for ilie coefficients i-r-^j &c.) identical 

with the equations of equilibrium of an elastic solid subjected 
to infinitely small strains, which have been given by Green, 
Cauchy, Haughton, and other writers. Many mathematicians 
and experimenters have endeavoured to show that in actual 
solids there are certain essential relations between these twenty- 
one coefficients [or moduluses] of elasticity. Whether or not it 
may be true that such relations do hold for natural crystals, it is 
quite certain that an arrangement of actual pieces of matter may 
be made, constituting a homogeneous whole when considered on 
a large scale (being, in fact, as homogeneous as writers adopt- 
ing the atomic theory in any form consider a natural crystal to 
he), which shall have an arbitrarily prescribed value for each 
one of these twenty-one coefficients. No one can legitimately 
deny for all natural crystals, known and unknown, any pro- 
perty of elasticity, or any other mechanical or physical pro- 
perty, which a solid composed of natural bodies artificially put 
together may have in reality. To do so is to assume that the 
infinitely inconceivable structure of the particles of a crystal is 
essentially restricted by arbitrary conditions imposed by mathe- 
maticians for the sake of shortening the equations by which their 
properties are expressed. It is true experiment might, and does, 
show particular values for the coefficients for particular bodies ; 
but I believe even the collation of recorded experimental inves- 
tigations is enough to show bodies violating every relation that 
has been imposed ; and I have not a doubt that an experi- 
ment on a natural crystal, magnetized if necessary, might be 
made to show each supposed relation violated. Thus it has 
been shown, first I believe by Mr. Stokes, that the relation 
which the earlier writers supposed to exist between rigidity 
and resistance to compression is not verified, because experi- 
ments on the torsion of wires of various metals, rods of india- 
rubber, &c. indicate, on the whole, less rigidity than would be 
expected, according to that relation, from their resistance to 

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cmd PyroeUctric Properties of Matter* 17 

compression, and less in different proportions for different 
metals. It is quite certain that india-rubber, jelly of any kind 
(ever so stiff), and guttap-percha are all of them enormously 
less rigid in proportion to their resistance to compression than 
glass or the metals ; and they are all certainly substances 
which may be prepared so as to be at least as homogeneous as 
rods, wires, Jbars, or tubes of metals. From some experiments 
conununicated to me by Mr. Clerk Maxwell, which he has made 
on iron wire by flexure and torsion, it appears highly probable 
that iron is more rigid in proportion to its resistance to com- 
pression than M. Wertheim's experiments on brass and glass 
show these bodies to be. 

[17. Since the publication of this paper, the same conclu- 
sion as to the relative qualities of iron and brass has been 
arrived at by Everett (Transactions of the Eoyal Society, 
1865 and 1866) as a result of fresh experiments made by him- 
self on these substances — ^but an opposite conclusion with re- 
ference to two specimens of flint glass upon which he experi- 
mented, and which both showed greater rigidity in proportion 
to compressibility than either his own experiments or tnose of 
others nad shown for iron or any other substance accurately 
experimented on. Far beyond these specimens of glass, witb 
respect to greatness of rigidity in proportion to compressibilitj*. 
is cork ; which though not hitherto accurately experimentea 
on, and though no doubt very variable in its elastic quality, 
shows obviously a very remarkable property, on which its use 
for corking bottles depends, viz. that a column of it compressed 
endwise does not swell out sidewise to any sensible degree, if 
at all. It is easy to construct a model elastic solid, on the 
plan suggested above, which shall actually show lateral shrink- 
ing when compressed longitudinally, and lateral swelling when 
pnued out longitudinally. The false theory, referred to above 
as having been first proved to be at fault by Stokes, gives for 
eveiT kind of solid \ as the ratio of the lateral shrinking to 
the longitudinal elongation when a rod is pulled out length- 
wise. The following Table (p. 18) shows how different are the 
values of that ratio deterinined by experiment on several real 
solids.] 

18. The known fact that fmany] gelatinous bodies, and the 
nearly certain fact that most bodies of all kinds, when their tem- 
perahires are raised, become less rigid to a much more marked 
extent than that of any effect on their compressibilities, are 
enough to show that neither the relation first supposed to exist, 
nor any other constant relation between conipressibilitj and 
rigidity, can hold even for one body at different tempera- 
tures. 

PhXL. Mag. S. 5. Vol. 5. No. 28. Jan. 1878. C 



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18 Sir W. Thomson on the Thermoelasticy Thermomagnetic, 



SubiUmoM. 



Attthorily. 



Batio of lateral shrinking 
or BweUing tolongitodinal 
extennon or shortening 
under the infltienoe of 
push or pull on ends of 
a column of the subetanoe. 



Cork 



'crystal 



SpeeimeoB of 

glM» 

A specimen of flint glass. 
Another speeimen of flint 

glass 

A specimen of brass 
Drawn brass rod ... 

Oopper 

Iron 

Steel 

Oaststeel 



Volcanixed india-rubber. 



General experience and 
some accurate measure- 
ments of diameter of a 
cork under yarious de- 
grees of end-pressure, 
producing shortenings 
from small amounts up 
to as much as ^ of the 
original length 

vWertheim 

BTeiett(1865) 

\BTerett(1866) 



Wertheim 

Everett (1866) 
W. Thomson ... 
Clerk llaxwell 

Kirchhoff , 

BTerett(1866) 

Joule 



•33 

•26 

•23 

•34 

•47 

from ^40 to -23 

•27 
•29 
•31 

{Less than '5 br an ez- 
ceedingljsmaU amount. 



19. Affain, some of the relations which have been supposed 
to exist lead to three principal axes of elasticity. Manj 
natural crystals do certainly exhibit perfect symmetry of form 
with reference to three rectangular axes^ and therefore pro- 
bably possess all their physical properties symmetrically with 
reference to those axes ; but as certainly many^ and amon^ 
ihem some of the best-known, of natural crystals do not exhibit 
symmetry of form with reference to rectangular axes, and pos- 
sess the mechanical property of resisting fracture differently in 
different directions, witnout symmetry about any three rectan- 
gular axes — ^for instance, Iceland spar, which has three planes 
of greatest brittleness ('^ cleayage-planes ''), inclined at equal 
angles to one another and to a common axis (the '^ optic axis '* 
of the crystal). If, as probably must be the case, the elastic 
properties within the limits of elasticity have correspondence 
witn the mechanical properties on whicn the brittleness in dif- 
ferent directions depends, the last-mentioned class of crystals 
cannot haye three principal axes of elasticity at right angles 
to one another. It will be an interesting inquiry to examine 
thoroughly the various directional properties of an elastic solid 
.represented by the different coeiScients (of which the entire 
number may of course be reduced from twenty-one to eighteen 
by a choice of axes), or by various combinations of them. 



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and Pyroelectric Properties of Matter, 1 9 

20. The general thermodynamic principles expressed above in 
the equations (6), (8), (12), and (13) enable ns to determine 
the relations between the evolution of heat or cold bj strains 
of any kind effected on an elastic solid, the variation of its 
elastic forces with temperature, and the differences and varia- 
tions of its specific heats. Thus (6) gives at once, when the 

development of tr expressed by (18) is used, and for (;t-) &c- 

are substituted P &c., which are infinitely nearly equal to them, 
the following expression for the heat absorbed by an infinitely 
small strainmg, namely from {x^y y^, z^j f ^^ i/^, Q to (a?, y, z, 

21. We conclude that cold is produced whenever a solid is 
strained by opposing, and heat when it is strained by yielding 
to, any elastic force of its own, the strength of which would 
diminish if the temperature were raised — ^butthat, on the con- 
trary^ heat is produced when a solid is strained against, and 
cold when it is strained by yielding to, any elastic force of its 
own, the strength of which would increase if the temperature 
were raised. When the stress is a pressure, uniform in all di- 
rections, fluids may be included in the statement. Thus we 
may conclude as certain: — 

(1) That a cubical compression of any elastic fluid or solid 
in an ordinary condition would cause an evolution of heat ; but 
that, on the contrary, a cubical compression would produce 
cold in any substance, solid or fluid, in such an abnormal state 
that it would contract if heated, while kept under constant 
pressure. 

(2) That if a wire already twisted be suddenly twisted 
farther, ^ways, however, within its limits of elasticity, cold 
will be produced ; and that if it be allowed suddenly to untwist, 
heat will be evolved from itself (besides heat generated exter- 
nally by any work allowed to be wasted, which it does in un- 
twisting). For I suppose it is certain that the torsive rigidity 
of every wire is diminished by an elevation of temperature. 

(3) That a spiral sprine suddenly drawn out will become 
lower in temperature, and will rise in temperature when sud- 
denly allowed to draw in. [This result has since been experi- 
mentally verified by Joule (" Thermodynamic Properties of 
Solids, Trans. Roy. Soc, 1858), and the amount of the effect 

02 

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20 SirW. Thomson on the Therrnoelastic^ Thermomaffnetic, 

found to agree with that calculated, according to the prece- 
ding thermodynamic theory, from the amount of the weaken- 
ing of the spring which he found by experiment.] 

(4) That a bar or rod or wire of any substance with or with- 
out a weight hung on it, or experiencing any degree of end 
thrust, to oegin with, becomes cooled if suddenly donated by 
end pull or by diminution of end thrust, and warmed if sud- 
denly shortened by end thrust or by diminution of end pull: 
except abnormal cases, in which, with constant end pull or end 
thrust, elevation of temperature produces shortening ; in every 
such case pull or diminished thrust produces elevation of tem- 
perature, thrust or diminished pull lowering of temperature. 

(4') That an india-rubber band suddenly drawn out (within 
its limits of elasticity) produces cold, ana that, on the con- 
trary, when allowed to contract, heat will be evolved from it. 
For it is certain that an indiar-rubber band with a weight 
suspei^ded by it will expand in length if the temperature be 
raised. [Alas for overconfident assertion ! This is not ti'ue — 
at all events not true in general for either natural or vulcanized 
india-rubber, but only true for india-rubber in somewhat ex- 
ceptional circumstances. It was founded on the supposition that 
india-rubber becomes less rigid when raised in temperature, 
which, besides, seeming to be expectable for solids generally, 
seemed to be experimentally proved for india-rubber by the 
familiar stiffness of common india-rubber in very cold weather. 
My original supposition is in fact correct for india-rubber 
which has become rigid by being kept at rest at a low tempe- 
rature for some time. In this condition india-rubber was 
found by Joule to be cooled when suddenly stretched, and 
heated when the stretching weight was removed ; and therefore, 
when in this condition, it is certain, from the thermodynamic 
principle, that a band of the substance bearing a weight will 
expand in length if the temperature is raised, and shrink when 
the temperature is lowered. But the very piece of india- 
rubber in which Joule found a cooling effect by pull when its 
temperature was 5° C, gave him a heating effect by pull, and 
a cooling effect on withdraw^al of pull, when the temperature 
Lwas 15° C. Joule experimented also on vulcanized india- 
rubber, and with it always found a heating effect when the 
substance was pulled out, and a cooling effect when it was 
allowed to shriuK back. I pointed out to him that therefore, 
by thermodynamic theory, a vulcanized india-rubber band, 
when stretched by a constant weight of sufficient amount 
hung on it, must, when heated, pull up the weight, and when 
cooled, allow the weight to descend. This is an experiment 
which any one can make with the greatest ease by hanging a 



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and Pyroelectrie Properties of Matter. 21 

few pounds weight on a common india-mbber band^ and taking 
a red-hot coal, in a pair of tongs, or a red-hot poker, and 
moving it np and down close to ihe band. The way in which 
the weight rises when the red-hot body is near, and falls when 
it is removed, is quite startling. Joule experimented on the 
amount of shrinking per degree of elevation of temperature, 
with different weights hung on a band of vulcanized india- 
rubber, and found that they closely agreed with the amounts 
calculated by my theory from the heating effects of pull, and 
cooling effects of ceasing to pull, which he had observed in 
the same piece of india-rubber. Joule's experiments leave 
the statements of the following paragraph (5) true for common 
india-rubber at 5° C, but reverse it for common india-rubber 
at higher temperatures and for vulcanized india-rubber — ^that 
is to say, leave it applicable to these substances with ^' pull " 
substituted for " push " throughout.] 

(5) We may conclude as highly probable, that pushing a 
column of indiar-rubber together longitudinally while leaving it 
free at its sides will cause the evolution of heat, when the force 
by which its ends are pushed together falls short of a certain 
limit ; but that, on the contrary, if this force exceeds a certain 
limit, cold will be produced by suddenly increasing the force a 
very little, so as to contract the column further. For I suppose 
it is certain that a column of india-rubber with no weight, or 
only a small weight on its top, will expand longitudinally when 
its temperature is raised ; but it appears to me highly probable 
that if the weight on the top of the column exceed a certain 
limit, the diminished rigidity of the column will allow it to de- 
scend when the temperature is raised. [This second change 
we now know to be contrary to the true state of the case ; for 
we have seen that the rigidity of india-rubber is augmented by 
elevation of temperature.] 

22. The specific heat of an elastic solid homogeneously strained 
under given pressures or tensions will be obtained ty finding 
the di^rential coefiicients of a, y, z, f , rj, 4 with reference to 
^, so as to make P, Q, R, S, T, U each remain constant or vary 
in a given manner — that is to say, by finding the coefficients 
of expansion in various dimensions for the body w4th an infi- 
nitely small change of its temperature, and using these in (3) 
above. 

23. The elastic properties of such a crystal as is frequently 
foand in natural specimens of garnet — a regular rhombic do^ 
decahedron — ^must, if they correspond to the crystalline form^ 
be symmetrical with reference to six axes in the substance 
perpendicular to the six pairs of opposite faces of the dodeca- 
hedron^ or to the six edges of a regular tetrahedron related to 



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22 Sir W. Thomson on the TliemweUxstiCf Thermomagnetic^ 

the dodecahedron in a determinate manner (having for its Gor- 
nerg four of the eight trihedral comers of the dodecahedron) ; 
and yet they may aiffer^ and in all probability they do differ, 
in different directions through the crystal. The relations 
among the coefficients of elasticity^ according to the system of 
independent variables used in the preceding paper, which are 
required to express such circumstances, may be investigated 
by choosing for the normal cube a cube with faces perpendi- 
cular to the lines joining the three pairs of opposite tetranedral 
comers of the dodecahedron. This choice of the normal cube 
makes all the coefficients vanish except nine, and makes these 
nine related one to another as follows : — 

W\ =w\ =(d?)o =^+2m, 

Vrfg /o \drjr/o \dKyo 



and 



\dt/ dz/o ^ \dz da/Q "" \dx dy/o "~ * 



where X, /i, ic are three independent coefficients, introduced 
merely for the sake of comparison with M. Lam^^s notation. 
In different natural crystals of the cubical system, such as 
fluornspar, garnet, <&c., it is probable that the three coefficients 
here left have different relations with one another. The body 
would, as is known, be, in its elastic qualities, perfectly iso- 
tropic if, and not so unless, the further relation 

/(Pw\ _(d^w\ . ofe") 
\d^)r UydzJo'^^Kd^Jo 

were fulfilled. Hence the quantity tc in the preceding formula 
expresses the crystalline quality which I suppose to exist in 
the elasticity of a crystal of the cubic class. 

24. The fact of mere being six axes of symmetry in cubic 
crystals (diagonals of sides of the cube), has suggested to me a 
system of inaependent variables, symmetrical with respect to 
those axes, which I believe may be found extremely convenient 
in the treatment of a mechanical theory of crystaUography, and 
which, so far as I know, has not hitherto been introduced for the 
expression of a state of strain in an elastic solid. It is simply 
the six edges of a tetrahedron enclosing always the same part of 
the solid f a system of variables which might be used in all ex- 

Sressions connected with the theory of the elasticity of solids, 
'o apply it to express the elastic properties of a crystal of the 
cubical class, let tne tetrahedron be chosen with its edges paralld 



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and PyroeUetric Properties of Matter^ 28 

to the six lines which are lines of symmetry when the solid is 
unstrained. In any state of strain let a,i/jzhe the lengths of 
three edges lying in one plane^ and (, rf, ^ those of the three 
oihers (which meet in a point). Let a^ Vq, Zq, f^, nj^., Jjj denote 
tilie yalnes (equal among themselves) of these yariables for the 
unstrained state, and let to be the work required to bring any 
portion of the solid (whether the tetrahedron itself or not is of 
no consequence) from the unstrained state to the state {x, y, z^ 
^jVj ^1^1^ ^®pt at a constant temperature. The relations 
amonff the coefficients of elasticity according to this system of 
variables, to express perfect symmetry with reference to the 
six axes^ will clearly be: — 

fiPw\ /€pw\ fd?w\ rcPw\ fdPw\ /d*«?\ 

\d^K " w A" Kd^jfT \drJo" wA" WK''"'' 

/(Ptg \ / d^w \ _ / cPw \ _ / cPw \ _ / cPw \ 
\rfy dzJo ^ \dz dx)^ \dx dy)^"^ \dt) rf{/o"! Kd^d^Jo 

didffJo'' \dx diy/o"" \dx d^/Q^ \dyd^o 

( cPw \ ^ / (Py^ \ ( dPw \ _ 

\ApdfA"" \dy dvJo'^ \dz dj/o""'* 

where «, Cy » denote three independent coefficients of elastioitr 
for the sabstance. The definition of the new system of van- 
ables may be giyen as simply^ and in some respects more con- 
Teniently, by referring to the dodecahedron, whose faces are 
perpendicular to the edges of the tetrahedron. Thus the six 
yariables x^y, z, f, 17, (^ may be taken to denote respectively the 
mutual distances of the six pairs of parallel &ces of the rhom- 
bohedron into which the regular dodecahedron is altered when 
the solid is strained in any manner. Thus, if the portion of the 
solid considered be the dodecahedron itself, and of such dimen- 
sions that when it is in its normal state the area of each face is 

nniiy, the values of ^ &c., denoted, as in the preceding paper, 

by P, Q, Ry S, T, U, are normal tensions (reckoned, as usual, 
per unit of area), on surfaces in the solid parallel to the feces 
of the dodecahedron, which compounded give the actual strain- 
ing force to which the solid is subjected. The coefficients 
denoted above by «, <r, eo are such as to give the following ex- 
pressions for the component straining tensions in terms of the 
strains :— 



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24 SirW. Thomson on the Thermoelastic^ ThermomagnetiCy 
P=fir(^-;j?o) + a)(e-fo)+^(y-yo + ^-^o+^-^o + ?-5i)); 

R=-Br(z-2ro) + ft)(f-?j) + <y(^-^o+y-yo + f-?o + ^-"'?o); 

T=w(i7-i;o) + a)(y-yo) + ^(-2^.-^o + «-^o + ?-?o + f-fo)5 

25. The three quantities, «r, 6>, o", or the three coefficients of 
elasticity according to the new system of independent variables, 
will express, by their different relative values, the elastic pro- 
perties of all crystals of the cubical class. For a perfectly iso- 
tropic body, a particular numerical relation, which I have noi. 
yet determined, must hold between «r, p, and <r ; and two inde- 
pendent coefficients of elasticity will remain. To detennine 
this relation, and to find the formulae of transformation from 
one set of variables to another on the new system, or from the 
new system to the ordinary system (that which was used in the 
precedmg portion of this paper), or vice versd, may be interest- 
mg objects of inquiry. 

Glasgow College, March 10, 1865. 

26. Extracted from NicIioVs ' Cyclopcedia of the Physical 
Sciences,^ second edition, 1860. Thermomagnetiam. (1) JKav 
perimental Facts. — Gilbert found that if a piece of soft iron 
between the poles of a magnet be raised to a bright red heat 
it loses all its ordinary indications of magnetism, and it only 
retains (Faradav, * Exp. Res.' 2344-2347) slight traces of the 
paramagnetic character. Nickel loses its magnetic inductive 
capacity very rapidly as its temperature rises about 635^ Fahr., 
and has very little' left at the temperature of boiling oil. 
Cobalt loses its inductive capacity at a far higher temperature 
than that of either, near the melting-point of copper. Of the 
three metals, iron remains nearly constant, nickel falls gra- 
dually, and cobalt actually rises in inductive capacity as the 
temperature is raised from 0° to 300° Fahr. (Faraday, ^ Exp. 
Bes.' 3428 ; ' Phil. Trans.' Nov. 1855). Cobalt, o^ course, 
must have a maximum inductive capacity at some temperature 
intermediate between 300° Fahr. and the temperature of melt- 
ing copper. Crystals, when their temperatures are raised, 
have their magnetic inductive capacities in different directions 
of the crystalline substance rendered less unequal, and in 
general to a very marked degree. Thus Faraday found the 
difference of inductive capacities in different directions in 
a crystal of bismuth (a diamagnetic crj'staH reduced to less 
than half when the temperature was raised from 100° to 280°. 



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atid Pyroelectrie Properties of Matter* 25 

In carbonate of iron (a paramagnetic crystal) the difference of 
indnctive capacities in aifferent directions was reduced to one 
third when me temperature was raised from 70^ to 289^ Fahr., 
and was tripled when the temperature was again brought down 
to 70° (Exp. Bes. 3400 and 3411). 

(2) Thermodynamio Relations. — The theory of the mutual 
convertibility of heat and mechanical work in reversible ope- 
rations when applied to these phenomena proves : — 1. That a 
piece of soft iron at a moderate or low red heat, when drawn 
gently away from a magnet experiences a cooling effect, and 
when allowed to approach a magnet experiences a heating 
effect; that nickel at ordinary temperatures, and cobalt at 
high temperatures, within some definite range below that of 
melting copper, experience the same kind of effects when sub- 
jected to similar magnetic operations. 2. That cobalt at ordi- 
nary atmospheric temperatures, and at all temperatures up- 
wards to its temperature of maximum inductive capacity, 
experiences a cooling effect when allowed to approach a mag- 
net slowly, and a heating effect when drawn away. 3. That 
a crystal in a magnetic field experiences a cooling effect when 
its axis of greatest paramagnetic or of least diamagnetic in- 
dnctive capacity is turned round from a position along to a 
position across the lines of force, and a heating effect when 
sncb a motion is reversed. 

[27. Let there be three rectangular axes fixed relatively to 
the movable body, whether soft iron, or copper, or a crystal 
in a magnetic field, and, considering the whole magnetic mo- 
tive * on the body, reduce it, after the manner of Poinsot, to 
three component forces along the magnetic axes and three 
couples round these axes. Let P, Q, R be the force-compo- 
nents^ and S, T, U the couple-components thus obtained, which 
we must suppose to be known functions of t, the temperature. 
Equation (22) of § 20 above gives H, the quantity of heat 
which must be supplied to prevent the body from becoming 
cooler when it is moved through infinitesimal spaces ^— ^q, 
y—t/Qj c— r^ in the directions of the three axes, and turned 
through infinitesimal angles f— fo> V^Voj 5"~?o round the 
same axes. The lowering of temperature which it experiences 

XT 

if heat is neither given to it nor taken from it is equal to p , 

where C denotes the whole capacity for heat of the body, or 
the product of its mass or bulk by its specific heat per unit of 

* [In dynamics the want is keenly felt of an expression for a s^-stem of 
forces acting on a body : adopting a suggestion of my brother, Professor 
James Thoniison, the word " motive '' is used in the text to supply this 
ttt] 



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26 On the Pt/roelectric Properties of Matter. 

mass or per nnit of bulk. If the directions of a?, y, z and 
f , f)y f are such that P, Q, R, S, T, U are positive, then for 
for iron and nickel, and for cobalt at temperatures above tiitA 
of its maximum inductive capacity. 



dp 


dQ 


dB. 


rfS 


dT 


dXJ 


~ dt' 


~ dt' 


dt' 


dt' 


dt' 


dt 



are positive, and therefore the substance experiences a cooling 
effect when it is moved in such a manner as to require work 
to be done against magnetic force ; and the reverse is the case 
for cobalt at ordinary temperatures.] 

28. Extracted from NichoVs ^ Cyclopaedia of the Physical 
Sciences J second edition, 1860. — The most probable account 
that can be given of the pyroelectric quality of dipolar crvs- 
tals is, that these bodies intrinsically possess the same kind of 
bodily electro^polarization which Faraday, in his ' Experimental 
Researches,' has clearly proved to be temporarily produced in 
solid and liquid nonconductors, and that they possess this 
property to different degrees at different temperatures. 

The inductive action exercised by this electro-polar state of 
the substance, on the matter touching the body all round, in- 
duces a superJScial electrification which perfectly balances its 
electric force on all points in the external matter ; but when 
the crystal is broken in two across its electric axis, the two 
parts exhibit as wholes contrary electrifications, not only by 
the free electro-polarities on the fractured surfaces discovered 
by Canton, but by the induced electrification on the old sur- 
face, belonging to the old state of electric equilibrium, and 
gradually lost by slow conduction, while a new superficial 
distribution of electricity on each fragment is acquired which 
ultimately masks all external symptoms of electric excitement. 
When the temperature of the substance is changed, its electro- 
polarization changes simultaneously, while the masking super- 
ficial electrification follows the change only by slow degrees — 
more or less slow according to the greater or less resistance 
offered to electric conduction in the substance or along its 
surface. 

[29. If the preceding explanation of pyroelectricity be 
true, it must follow that a pyroelectric crystal moved about 
in an electric field will experience cooling effects or heating 
effects calculable by formula (22) of § 20, with the same no- 
tation for the electric subject as that of § 27 for magnetism. 
Thus the effects will be the same for a crystal at the sa^ne tem- 
perature whatever be the electrification of its surface. Tbaa 
it is remarkable that, in virtue of the wholly latent electric 



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Mr. J. Le Conte on Binocular Vision. 27 

polariiy of a seemingly neutral pjroeleciric crystal (that is 
to sajf a crystal at the surface of which there is an electrifi- 
cation neutralizing for external space the force due to its in- 
ternal electric polarity), the same cooling and heating effects 
will be produced by moving it in an electric field, as similar 
motions would produce in a similar crystal which, by having 
been heated in hot water, dried at the high temperature, ana 
cooled, is in a state of pyroelectric excitement.] 

Yacht 'LallaRookh/ 
Laiga, Sept 18, 1877. 



III. On BinocularViaion 
To the Editors of the Philosophical Magazine and Journal. 

GSNTLEIOEN, 

IN Mr. Thompson's excellent article on the Chromatism of 
the Eye, in the July Number of your Journal, I notice 
the following sentence : — '^ In Wheatstone's classical research 
of 1838 it was demonstrated how great is the capacity of the 
brain to combine two slightly differing retinal images.'* 
From this sentence I conclude that Wheatstone's theory of 
binocular relief is still held by many scientists : I am con- 
firmed in this conclusion by finding the expression '^ mental 
fusion " or " conscious fusion " of dissimilar images in nearly 
all works on the sulyect, even the latest, viz. Hermann^s ^ Phv- 
siology.' Now, as I am quite sure that this theor}'^ is not only 
untenable, but positively hurtful to science by discouraging 
that careful analysis of visual perception so necessary to a true 
theory and yet so difficult to most persons, I have thought it 
would not be amiss to state briefly what I conceive to be the 
present condition of science on this subject. 

In all investigations on binocular vision we are met at the 
very threshold by the difficulty which most persons find 
in analyzing what I would call visual judgments, i. e. judg- 
ments which by long habit and inherited tendency seem at 
first to be direct sensuous perceptions incapable of iurther 
analysis. It is difiicult to convince many persons that they 
ever see double images at all ; and yet they, of course, every 
day form judgments based on the existence and the uncon- 
scious perception of such double images. It is difficult to 
convince most persons, even the thoughtfiilly observant, that 
in regarding a stereoscopic scene there is no complete fusion 
of the two pictures, but that, when the eye is fixed on the 
foreground, objects in the background are double, and vice 



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28 Mr. J. Le Conte on Binocular Vision. 

versd. It is still more difficult, nay, almost impossible, eyeii 
for those accustomed to analyze these visual perceptions, to 
perceive a similar partial doubling of images in regarding an 
actual solid object. Yet by careful analysis we may convince 
ourselves of all this. Nothing can be more certain than the 
fact that the complete fusion of dissimilar images never takes 
place, and that, if we think otherwise, it is only because we 
do not observe and analyze carefully. 

From early boyhood 1 have accustomed myself to make ex- 
periments on binocular vision, and have thus gradually acquired 
an extraordinary aptitude in decomposing complex visual 
judgments into their component sense-impressions. In com- 
binations of stereoscopic pictures, whether in the stereoscope 
or with the naked eye by squinting (t. e. whether beyond or 
on this side the plane of the pictures, and therefore whether 
the binocular relief be natural or inverted)^ I always distinctly 
perceive the doubling of parts of the scene or object when a 
nearer or a more distant part is regarded. Also in viewing 
natural objects, even such objects as small cones or prisms, 1 
always perceive the doubling of the nearer parts while regard- 
ing the further parts, and vice versd. Wheatstone's theory 
therefore seems true only to the unobservant or unpractised: 
it is a popular explanation, not a scientific theory ; it cuts, but 
does not loose the Gordian knot. 

Briicke and Brewster, by more refined observation and 
more careful analysis, easily perceived that there was in reality 
no mental fusion of two dissimilar images. Their view is that, 
in regarding a solid object or two stereoscopic pictures, the 
eyes are in mcessant unconscious motion, by greater and less 
optic convergence successively combining the different parts 
of the two images, and thus by ranging back and forth reach 
by trial the distinct perception of binocular relief. 

This theory is undoubtedly a great advance upon Wheat- 
stone's. It is really a scientific theory, since it is based upon 
an analysis of our visual judgment. It is also in part a true 
theory : but it is evidently not the whole truth ; for successive 
trial-combinations of difierent parts of the two images are not 
necessary to the perception of binocular perspective. The ex- 
periments of Dove have proved that binocular relief is dis- 
tinctly perceived even by the light of an electric spark, which 
lasts only zj^^^^ of a second — a time too short to allow any 
change of optic convergence. 

I have repeated these experiments of Dove with great care, 
with the double object of testing their accuracy and at the 
same time of testing the truth of a view which I had pre- 



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Mr. J. Le Conte on Binocular Vision. 29 

vionsly formed on this subject. My experiments completely 
confirmed the results of Dove. I found that binocular relief, 
both by combination of stereoscopic diagrams ^whether in the 
stereoscope or by the naked eye) ana by viewing natural 
objects, b indeed perfectly distinct by the light of the electric 
spark ; but I also observed in all cases the doubling of the 
nearer lines or objects while regarding the more remote, and 
vice versa. 

Between the two rival theories, then, the matter stands 
thus: — ^Wheatstone is right in so far as he asserts immediate 
perception of relief, but is lorong in supposing any mental 
f^ision of the two images. Briicke is right in asserting that 
the perception of binocular relief is a judgment based upon 
double images of all parts of the object or scene beyond or on 
this side the point of sight, but is wrong in supposing that 
change of optic convergence and successive trial combination 
is a necessary part of the evidence on which judgment is based. 
My own view, or theory if I may so call it, has already been 
published*. It is an attempt to unite what is true in the two 
preceding views. I quote from a previous paper: — "All 
objects or points either beyond or on this side tne point of 
sight are doubled, but differently — the former homonynwuslyy 
the latter heteronyrtiously ; the double images of the former 
are united by less, of the latter by ^/r^afer convergence. Now 
the observer knows instinctively arid without tricdy in any case 
of double images whether they will be united by greater or by 
less convergence, and therefore never makes a mistake, or 
attempts to unite by a wrong movement of the optic axes. 
In other words, the eye (or the mind) instinctively distinguishes 
between homonymous and heteronymous images, re/erring the 
former to objects or points beyond, and the latter to objects or 
points on this side tlie point of sight. The mind therefore per- 
ceives relief tn«ton^/y by means of double images in the manner 
just explained ; but the perception is doubtless made clearer by 
changes of optic convergence, by ranging the eyes back and 
forth from foreground to background and vice versa, and the 
saccessive combination of different parts of the object or pic- 
tares, as maintained by Briicke.'' 

1 am, Gentlemen, 

Yours very respectfully, 

Berkeley, California, JoSEPH Lb Contk. 

November 17, 1877. 

^ Amer. Journ. vol. ii. pp. 1, 315, 417 ; Archives des Sciences, vol. xlL 
p. 394 (1871). 



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[ 30 ] 

rV. Electromagnetic and Ccdometrie Absolute Measurements: 
the Absolute Value ofSiemen^s Unit of Resistance in Electro^ 
magnetic Measure ; the Relation between the Current-work 
and the Heat-evolution in staiionary Galvanic Currents ; and 
the Absolute Values of some constant Hgdroelectromotive 
Forces in Electromagnetic Measure. (Condensed Comparison 
of the Results of a Series of Investigations.) By H. F. 
Weber, Professor of Mathematical and Technical Physics 
at the Federal Polytechnic Academy of Zurich *. 

SINCE Siemens^s unit of resistance has been admitted into 
the department of galvanic measurement's^ the attempt has 
been made in four different quarters to fix the absolute value 
of this empiric unit — ^that is, to determine in absolute measure 
that electromotive force which, in a conductor whose resistance 
is equal to that of Siemens^s unit, is capable of calling forth a 
current of absolute intensity. 

1. The fundamental system of measurement was the elec- 
tromagnetic. 

In 1862, W. Weber, according to a method devised by 
himself {Abhandlungen der Gdttinger Gesellschaft, Band x.), 
found as the absolute value of the Siemens mercury unit : — 

1 S. M. U.=l-0257 X W /5»!!™'\ 

\ sec. / 

According to the same method, and by aid of the same in- 
struments, F. Kohlrausch t, eight years later, repeated the 
determination, and, from four different measurements^ obtained 
as the mean value 

1 S. M. U.«0-9717 X 10^« /eIHIEiV 

\ sec. / 

The committee appointed by the British Association for the 
Advancement of Science to determine upon a suitable unit of 
resistance, consisting of Messrs. Clerk Maxwell, Balfour 
Stewart, and Jenkin, in ihe course of the years 1863 and 1864 
produced a resistance, the British-Association unit (by English 
physicists called also the " ohm "), which is said to represent 
in electromagnetic measure exactiy the absolute value 10^® 

( -). According to the best comparisons^ this British 

unit is to the Siemens as 1 : 0*9536 ; consequently, according 
to the measurements of the English physicists, the absolute 

* Translated from the German original communicated by the Author. 
t Pogg. Ann, Eig.-Band vi. p. 1. 



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J^edromoffTiHic and Calometric Absolute Measurements. 31 

Taloe of Siemens^s unit would be equal to 0*9536 x 10^^ 
/ millimA 

* 06C» / 

More recently M. Lorenz^ in Copenhagen, by a very simple 
method peculiar to himself*, in which induced currents of 
constant strength were employed, has measured the magnitude 
of the Siemens unit of resistance in absolute electromagnetic 
measure^ obtaining as the final result of his measurements : — 

1 S.M.U.=0-9333xlO»« /millina.\ 

\ sec* / 

How many different observers have determined the absolute 
qnantity of the Siemens resistance-unit, so many different, 
indeed very different, results have been found. With the 
delicacy now attained of galvanometric methods of observation, 
wifli the completeness with which we believe we understand 
flie fundamental laws of current-electricity, certainly no one 
anticipated that in the final results of physicists so practised 
in this kind of work there could appear so great a divergency. 
These four different results, when compared, present a new 
problem, and one of fundamental importance for galvano- 
metrv. The two h priori equally possible solutions of the 
problem are : — 

(a) The four observers, or groups of observers, have carried 
out Uie difficult observations requisite for a determination of 
the absolute resistance without error ; and the final results 
differ because the natural laws assumed as the basis of the 
dififerent methods of observation are not precisely the true 
Or 



(b) The natural laws employed are rigorously correct, and 
•i least three of the above observers have committed some 
error. 

In the following investigations it is found that the latter 
solution is the true one. Gmree essentially different methods, 
which brought into application three quite different natural 
laws, and in which both rapidly and slowly varying induced 
currents and also stationary flows came into use, have given a 
perfectly aecordant final result for the absolute value of the 
Siemens resistance-unit — ^namely, 

1 S. M. U. =0-9550 X 10^« (^^^) . 

\ sec. / 

and, besides, this result agrees, except an extremely slight 
difference, with the value obtained by the English physicists. 
Since, even with manifold variation of my three methods of 

* Pogg. An$k vol. cxlix. p. 261 (1873). 

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32 Prof. H. F. Weber on Electroniaynetic and 

experiment^ I was unable to efiect any material change in my 
final result, I am compelled to see, in the divergent results of 
MM. Wilh. Weber, F. Kohlrausch, and L. Lorenz (who more* 
over conducted the investigation each according to on^ method 
only), values affected with errors of observation. 

I. Determination of the Absolute Vahie of the Siemens Resist- 
ance-Unit on the basis of t fie Laws of Magneto-Induction. 
As my first method of experiment for the determination of 
the value of the unit in question I chose a procedure which 
had already been employed by Wilhelm Weber on the intro- 
duction of absolute measurements of resistance * ; and I 
managed it so that it could be carried out under two different 
conditions. 

Two exactly equal, extremely regularly wound cylindrical 
spirals were connected with a multiplier so that their axes fell 
into one and the same horizontal straight line, which was per- 
pendicular to the magnetic meridian. The inner radius of 
the spirals wa3 144*43 millims. ; the outer radius amounted to 
184*46 ; the depth of the space occupied by the turns amounted 
consequently te 40*03 millims. ; its breadth was 53*64 millims. ; 
and each spiral numbered 691 turns. A most powerful paral- 
lelepipedal magnet (its length, breadth, and height were 80, 
20*1, and 21*1 millims. respectively) was placed with its centre 
exactly in the axis of the two spirals, and as nearly as possible 
in the middle between the central planes of the latter ; it wajs 
supported ]by a thin brass wire of about 3 metres length. The 
stated dimensions of the multiplier and the magnet are of such 
a magnitude that, in the calculation of the mutual taction 
between multiplier and magnet, in the place of the latter a 
system of two magnetic poles of equal magnetic moment could 
be put. 

If a magnet within a multiplier be rotated a small angle 
from its position of equilibrium and left to the forces acting 
upon it, it will describe isochronous oscillations, the amplitudes 
of which diminish in a geometrical progression. With the 
multiplier " open '^ 
the oscillation-period 



/MH B /Ay' 



and ihe logarithmic decrement of the amplitndes I 
* EUctrodynamische Maasthestimmu/nffen, p. 232. 

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(1) 



Calotnetric Absolute Measurements. 33 

According to the law of magneto-indaction^ with the mul- 
tiplier " closed " 

the oedUatioD-period ^ 

TT 



*~^ /MH^B/M*GP^ A\^ 

and the logarithmic decrement of the amplitudes 
/M^ A\ 



(^) 



In these eqnations^ K denotes the moment of inertia^ and M 
the magnetic moment, of the magnet ; H the horizontal com- 
ponent of the earth's magnetic mrce ; B the torsion-moment 
of the snspension-wire ; A the rotation-moment with which 
the wire and the sorroanding medium act upon the magnet 
moved with the angular velocity 1 ; G the electromagnetic 
force with which the multiplier, when the current 1 flows 
through it, acts on the magnetic unit of mass concentrated in 
one polar point ; and w the absolute value of the resistance of 
the multiplier (in electromagnetic measure). 

From equations (1) and (2) result the further equations 

T Ti " 2K«7 ' 
and 

Tj "" t; ' 

and from these we get^ for the absolute resistance w the ex- 
presfiion 

which^ according to equation (1), can be replaced bj 



«7 = 



where denotes the quantity ^=^^. If the resistance of the 

multiplier has been found equal to n Siemens mercury units, 
PhU. Mag. S. 5. Vol. 5. No. 28. Jan. 1878. D 

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84 Prof. H. F. Weber on Eleciromaqnetic and 

then the absolute value of one Siemens mercur7unit(lS.M. U) 
in electromagnetic measure is : — 

1S.M.U. = — .^..T,-^.— ^c. j.==^^ (4) 



n H 2Ti(l + tf) r~7P^ 



Strictly, in the development of the absolute value for w 
account would also have to be taken of the fact that the cur- 
rent induced primarily by the movement of the magnet b 
variable with the time, and in consequence of this acts indu- 
cingly on its own path. The carrying-out of the calculation 
shows that the influence of this induction of the induced cur- 
rent is so small in comparison with the other conditioning 
moments, that the expression above given for w is, in conse- 

Suence thereof, only increased by (in round numbers) ^^t^^^ . 
iince, in the measurements cited below-, none of the quantities 
to be determined could be measured with such accuracr^ that 
an additional vj^^j^ of its value could have been safely esti- 
mated, the influence of the induction on the part of the pri- 
marily induced variable current might be completely ignored. 
For the determination of the absolute value of the S. M. U. 
by means of this procedure there are consequently seven dif- 
ferent quantities to be measured. 

The five quantities Xi, Xj, Ti, (1 + ff), and ( tj ) were deter- 
mined by the method introduced by Grauss. The value of G 
was calculated, by means of the fundamental law of electro- 
magnetic action at a distance, from the dimensions and form 
of uie multiplier : 



^ 2imB? 



iR3j 3 Pr4D»~R» hU5 14 B? 4D»-RV 21 ^ 21 P 

y-i ip^L p^ p^ts "3 />«■*■ p^ U'*"2y 

I 6^r4 56 D» 4D'^-RV7 21 D^)"!^ 
[■^/^Is""^ 7 p'~~\6^~2y))J^''' 

Here n denotes the number of the turns of the multiplier, 
R the mean radius of the turns, 2D the distance between 
the central planes of the two spirals, 2A the height, and 26 
the breadth, of the cross section of the space occupied by 
the turns, p the quantity \/R* + D*, and 21 the distance be- 
tween the poles of the oscillating magnet. 



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Calometric Absolute Measurements. 35 

In deriving this expression it was presupposed that in place 
of the spiral tarns circular turns might be put continuoasly 
filling the space occupied by the multiplier ; further, the angle 
u of the deflection of the magnet was taken as so small that 
one might put 006u=l and 5sin*M vanishingly small in 
comparison with 1. In the observations carried out u never 
exceeded the value 2°. The cylindrical spirals were so con- 
stnicted and set op that the lengths B, D, ft, and 6 could be 
accurately measured to within 0*1 millim. directly with the 
cathetometer. 

The number n of the Siemens units which represented the 
resistance of the multiplier at the time of each observation 
was determined by aid of a bridge arrangement, which most 
carefully excluded all errors that might happen from extra 
currents, variations of temperature, dissimilar positions of the 
measuring-wire, the presence of transitory resistances, &c. 

Eighteen series of experiments were carried out, according 
to this process, on 18 different days. The following was 
always the order of the operations: — determination of the 

numbern; ascertaining of (^j and Z ; then determination of 

the values Ti, Xi, Xj from twelve successive series of observa- 
tions with the multiplier alternately " open " and '^ closed ; " 

and, lastly, repetition of the measurement o{(^), l^and n. 

The temperature of the observation-room never varied during 
any one series of experiments more than 0°*6 at the most, and 
was of course closely followed. 

In order to get some light upon the trustworthiness of the 
results obtained by this method, two groups of experiments 
were instituted. In the Jirst group the two spirals were 
poshed as near together as the suspension-wire of the magnet 
permitted (to the distance D=39*2 millims.); with this the 
difference Xj— Xi proved to be, on the average, 0*0296. At 
the same time the term 

_3Pp4D*-R? A^f 5 14 R^ . 4D^~RV 21 . 21 W\\ 

y f 4 56 D^ 4D^~RY 7 21 D^ \-i 
■^'pHS 3 p^ p" V6 2 pV jJ 

in the above-given general expression for G had here a value 
(about 2 per cent.) which togetner with the initial term 1 added 
considerably to its importance. 

D2 

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36 Prof. H. F. Weber on Electromagwtxe and 

There were found : — 

April 4,1876, 1 S.M.U. =0-9551x 10^» (^^)- 



„ 5, „ r=0-9532xlO^'> 

6 =0-9570 X 10^" 

" 7 =0-9565 X lO^" 

" 8, =0-9548 xlO^o 

" - =0-9555x10^" 






„ 10, 
The mean value of these six series is 

1 S.M.U. =0-95535x10^°. 

In the second gi-oup of trials the spirals were pushed so far 
asunder that the distance between their central planes teas as 
closely as possible equal to the mean radius of their unndinffs. 
Fortiis position of the spirals (2D=164'4 millims. nearly) 
the difference of the logarithmic decrements amounted to only 
about 0-0172 ; at the same time the expression of G was a/>- 
proximately independent of the pole-distance of the magnet : 

for the case that I^= o' 

^ 16^. nr, 1 A' 3P /36 6«_31A»\-l. 
^=5757rL1"15B? + 4^'Vi5? 15^;J' 

and the value of the last member within the square brackets 
amounts to only — 0*00028. 

The results found with this arrangement of the experiments 
were: — 

April 12, 1876, 1 S. M.U. =0-9531 x 10^» (^^^')- 

13, „ =0-9543 xl0»» „■ 

14, „ =0-9542x10" „ 

15, „ =0-9534x10" „ 

16, „ =0-9555 xlO»» „ 

17, „ =0-9528x10" 

The mean valae amounts to 

1 S. M.U. =0-95388 x 10" (^^^•). 

\ sec. / 

During the summer of 1876 the multiplier was taken to 
pieces ; in the autumn I once more subjected all the dimen- 
sions of both spirals to a cathetometric examination, and again 
put the spirals together so as to form a multiplier of the sort 
last described. The moment of the magnet had, in conse- 
quence of continual use at different times, become so consi- 
derably diminished that the difference of the logarithmic de- 
crements Xj— \i now amounted to only about 0'0161. 



Digitized by VjOOQIC 



Calometrie Absolute Measurements. 37 

The results found in this third series were : — 

Sept. 15, 1,876, 1 S. M. U. =0-9551 x 10^^ (^^^)- 

„ 16, „ =0-9550 xlO^o „" 

„ 17, „ =0-9548x10^^ „ 

„ 18, „ =0-9527x10^° „ 

„ 19, „ =0-9538x10^^ „ 

„ 20, „ =0-9544x10^° „ 

According to these, in the mean, 

1 S. M. U.=0-95430 x 10^° rElliErY 

V sec. / 

The total result of all the measurements is : — The absolute 
Talne of the Siemens resistance-unit, in electromagnetic mea- 
sure, derived from the electromotive forces and me galvanic 
carrents which are induced by slow oscillating movements of a 
magnet in a linear conductor in its vicinity is, in the mean 

from eighteen series of trials, 0'95451 x 10^^ ( * )• 

n. Ascertainment of the Absolute Value of the Siemens Mercury 
Unit by aid of the Laws of Voltaic Induction. 

Notwithstanding the perfectly satisfactory accordance of 
the individual results of the experiments decribed in section 
I., I have yet derived the absolute value of Siemens's empiric 
resistance-unit bv a second, essentially different method. W bile 
in the first metliod the laws of magneto-induction^ produced 
by slow motion of a magnet were employed, in the second the 
laws of voltaic induction, generated by rapidly varying gal- 
vanic currents, were used. 

The two large cylindrical spirals which in the previous ex- 
periments had served as multiplier, were in these new experi- 
ments set up so that their axes fell into one and the same 
straight line, and their middle planes had a certain distance D. 
One of the spirals, the inducing, together with a simple circular 
ring of 165*7 millims. radius, was inserted in the circuit 
of a DanielPs pile, which was so constructed that it furnished 
for hours an almost absolutely constant current. The other, 
ihe induced spiral, formed with a third large cylindrical spiral 
of 370 windings a closed circuit. The last spiral was com- 
pofled of two exactly equal halves, separated by a narrow in- 
terval. The radius of the innermost turn of this spiral was 
154'^ millims., that of the outermost 172-22 millims. The 
space occupied by the windings had a rectangular cross section 
of the breadth of 33*5 millims. ; the central planes of the two 
halves were distant from each other 20*75 millims. Exactly 
in the middle of the interval separating the two halves was 
placed the above-mentioned circular ring of the radius 165*7 

Digitized by VjOOQIC 



38 Prof. H. F. Weber on EUctromagnetic and 

miUims. ; its plane was parallel to the tarns of the spiral ; its 
centre was on the axis of the latter. A small magnet of 40 
millims. length was suspended, by a single cocoon-thread, ex- 
actiy in the middle of the spiral. 

lie following was the method of experiment : — ^The indnced 
circuit being open, a constant current was produced in the 
inducing circuit, the intensity of which, I, was measured in 
absolute measure by the action of the ring upon the little 
magnet. Then the inducing circuit was opened, the magnet 
brought to rest, the ring taken out of the inducing circuit and 
the latter again closed. After the path of the induced current 
was also closed, the inducing current I was opened ; the in- 
duction-current called forth by the sudden sinKing of the in- 
tensity of the inducing-current to zero was measured by its 
integral current. Hereupon the inducing current's intensity 
I was again determined, and so on. Thus were taken from 
20 to 30 successive measurements of the inducing current's 
intensity I and of the integral current y, generated by opening- 
induction. In none of the series of experiments carried 6ut did 
the intensity I vary, in the coarse of from one to two hours, 
more than about ^ per cent. 

The calculation of the induction-processes thus excitdd was 
based Qjpon the following assumptions : — 

(1) The course of the induction produced by sudden altera- 
tion of current-intensity in the inducing circuit is perfectly 
represented by the general law of induction set forth by F. E. 
Neumann ; and 

(2) The induced current called forth by this extremely 
rapidly passing induction fulfils Ohm's law. 

Mr. F. E. Neumann, in his treatise Die matJiematisehen 
Gesetze derinducirten.electrischenStrdmeyhs^d not more closely 
investigated this kind of induction. He says, ^^ So far as these 
formulae admit of being applied to those cases in which a gal- 
vanic current suddenly appears or is interrupted, further ex- 
perimental trial is required ; for they presuppose that the 
velocity with which the inducing cause enters is inconsiderable 
in comparison with the velocity of propagation of electricity 
in an induced conductor. On the assumption of the applica- 
bility of formulae (Ifi) and (17) to the mduction occasioned 
by tne sudden rise or disappearance of galvanic currents, we 
can say that the current induced in a conductor at rest by the 
sudden appearance of a galvanic current is the same as if the 
conductor had moved towards the current, from infinite dis- 
tance to the place where it is." That currents induced by 
swiftly-passing fluctuations of a current actually range them- 
selves nnder Neumann's general law of induction, and at the 
same time indeed foUow Ohm's law, Helmholtz (in his memoir 

Digitized by VjOOQIC 



Calametrie Absolute Measurements. 39 

on tlie daratioQ and course of electrical currents indaced by 
carrent-intermissions) showed^ some years later, by a series of 
measurements. Since the question whether the induced 
cnrrenis originated by sudden current-intermissions exactly 
iidlow Ohm's law or not, cannot be theoreticaUy decided uni- 
versally, but only be answered empirically in each individual 
case, I have, in order to gain a perfectly sure foundation for the 
measurements attempted, first instituted, in a preliminary in- 
vestigation, as severe a tnal as possible of how far the currents 
induced by sudden opening of the inducing circuit, in my 
arrangement of the experiments, follow Ohm's law. In this 
preliminary investigation nothing could be perceived that 
would intimate that induced currents arising from sudden 
current^variations do not exactly follow Ohm's law. 

If Iq denotes the current-intensity whose sudden diminution 
to zero effects the induction, P me mutual electrodynamic 
potfflitaal of the two spirals, if t represents the induced-current 
mtensity present at the moment t of the induction^process, 
and w the resistance of the induced circuit, then is the 
equation 

to\ i.dt^w.j=T?.lQ (1) 

(if we suppose that the induction commences at the moment 
1=0 and has already finished at the moment ^=^i) the re- 
sulting expression which is gained as soon as Neumann's 
general law of induction and Ohm's law are applied to the 
process of ^^ opening "-induction. The absolute measurement 
of w in electromagnetic measure was carried out according to 
this equation (1). 

The electromagnetic potential of the two spirals has the 
value 



'-If^ 



where dsi denotes any linear element of the one spiral, ds^ any 
element of the other spiral, r the distance between these ele- 
ments, and V the ancle which their directions make with one 
another, and where me integration has to be extended over all 
the elements of both spires. Into the somewhat lengthy 
working-out of the calculation of the quantity P we do not, in 
this abstract, enter farther. 

The absolute electromagnetic value of the current-intensity 
]q is obtained from the deflection-angle u, measured by aid of 
mirror, scale, and telescope : 

'.-2^»=('+m)(i-|E>)'"-' 

Digitized by VjOOQIC 



G=:^ 



40 



Prof. n. F. Weber on Electromaffnetic and 



where B denotes the moment of torsion of the cocoon-thread, 
M the magnetic moment^ and 21 the distance of the pole- 
points of the small magnet. 

J£ we call T the duration of an oscillation of the small mag- 
net, X the logarithmic decrement of the amplitudes of the 
oscillating magnet in the closed multiplier, G the electro- 
magnetic force with which the multiplier, passed through hj 
the current 1, acts upon the magnetic unit of mass ( + 1) pre- 
sent in one pole-point of the magnet, and, lastly, a the arc 
which the magnet describes from its position of rest in conse- 
quence of the action of the induced integral current/, then 
the absolute electromagnetic measure of Sie integral current 
generated 

According to this, we have for the absolute value of to z — 
B«('-iff) 



tr=P. 



tanu 



2T.6^ 



r.n.r 



For the multiplier used, G had the value 



3 pn 



>»L3 3 
4D»-r» 



21D»> 



(t-T?)] 



,1 



a-¥^}] 



Vci 56 D» 

and there were 

n=370 

r=:163'2 millims. 
p= 164-5 „ 
D= 20-7 „ 

To find the valne of the Siemens unit of resistance in absolute 
measure, two ways of proceeding were adopted : — 

(1) Tie resistance w was measured in Siemens mercury- 
units by the bridge method. It was found that to was equal 
to m Siemens units. Thus the absolute value of 



2/t=18-0 millims. 

2i=33-5 

21 =33-0 






1S.M.U= 



P.B.G 



(-IS) 



tanu 



m 



A 



Digitized by VjOOQIC 



Cahmetrie Absolute Measurements, 41 

(2) A completely stoppled Siemens stopple-rheostat was 
inserted in the induced circuit, and first the arc a determined 
which was given as deflection with the total resistance w of 
the induced circuit ; upon this, without making any change 
in P, R, G, u, &c., 10 8. M. U. of the rheostat were inserted 
in the induced circuit in addition to w. If then the arc of 
deflection was ai, the absolute value of 

P.R.G(l-f^Wnu - . 
10 S. M. U. = ^ \^' (^1- 1\ 

According to each of these two proceedings two series of ob- 
servations were made — the one with the employment of a very 
great potential-value P and a moderate intensity Iq of the in- 
ducing current, the other with the employment of a compara- 
tively small potential-value P and an extremely great inten- 
sity lo of the inducing current. As absolute value of the 
Siemens unit there was found : — 

Series I. 

P large, Iq moderate. 

Method 1. 

Aug. 20, 1876, 0-9558 xlO^«(^?^^l^-y 

\ sec. / 

„ 21, „ 0'9536xlOW „ 

„ 22, „ 0-9559 xlO^» „ 



„ 23, „ 0-9581 xlO^o „ 
„ 24, „ 0-9563 xlOi« „ 
„ 26, „ 0-9549 xlO^' „ 

The mean value amounts to 0-9557 x W f °"'^™' V 

\ sec. / 

Series 11. 

P large, \ moderate. 

Method 2. 

Aug. 20, 1876, 0-9516 X 10^" (5^^*\ 

\ sec. / 

„ 21, „ 0-9545x10" „ 

„ 22, „ 0-9550x10" „ 

„ 23, „ 0-9575x10" „ 

„ 24, „ 0-9556x10" „ 

„ 26, „ 0-9552x10" „ 

The mean value is 0-9549 x 10^*> 



» 



Digitized by VjOOQlC 



42 Electromagnetic and Calometric Absolute Measurements. 









Series III. 










P moderate, Iq large. 












Method 1. 






Sept. 


28, 


1876, 


, 0-9525 X 10" ("""^ 
\ sec. 


^ 


9} 


29, 


» 


0-9546x10" 


99 




99 


30, 


f} 


0-9581 y 10" 


99 




Oct. 


1, 


f} 


0-9552 X 10" 


99 




79 


3, 


f) 


0-9557 X 10" 


99 




99 


4, 


99 


0-9560x10" 


99 




The mean value is 


0-9550x10" 


>> 










Series IV. 










P moderate, lo large. 












Method 2. 






Sept. 


28, 


1876 


, 0-9568 X 10" fH^'l™ 
' \ sec. 


'•) 


99 


29, 




0-9561 X 10" 


99 




99 


30, 




0-9541 X 10" 


99 




Oct. 


1, 




0-9552x10" 


99 




V 


3, 




0-9543x10" 


79 




V 


4, 




0-8589 X 10" 


w 




The mean valne is 


0-9559x10" 


91 





The final results of these measurements, effected under very 
diverse circumstances, agree within vanishingly small differ- 
ences. They furnish the total result, that the absolute value 
of the Siemens empirical unit, derived from what takes place 
in voltaic induction called forth by sudden variations of cur- 
rent, amounts to 0-9554 x 10^« (5^^™-). 
' \ sec. / 

On the basis of the laws of magneto-induction, according to 
the first metliod, we had found as the absolute value of 

Siemens's resistance-unit the quantity 0*9545 x 10^® ( ' j > 

this value accords to within j^T ^^ ^** amount with that 
found by the second method. On account of the frequent 
repetition and manifold variation of the experiments, it may 
well be taken as sufficiently certain that this accordance is not 
accidental. From the almost perfect accordance of the final 
results obtained by the two methods two important conclusions 
can be drawn : — 

(1) The fundamental laws hitherto recognized of indnced 
currents of variable intensity represent with great precision 



Digitized by VjOOQIC 



JUNITER^I'^^' OF 



Digitized by VjOOQIC 



Phfl.Ma^.S.5. Vol.5. Pl.II. 




J -11' -10 



J}otbul Lints 

GmiinuutuM Linme . 



ar> Capaeity Curvets. 
. arm CondtuHuniy Gjurym- 



JRnnt A. ahcvJtt 0'002 miero-^MixueU eapaa'ty ptr oubv& otniimjUr*., 
Aint £ cdfout 0-1185 Tfauarc-famAM oapottuty pr cubic ctnJDanatr*, h 
R/inJb F ahouJb 2240 •m^oTtntm r»»istanom pwr cubic. otniimiU^ 
J*oinb K eibeut 0'S4- -mMyohntB rmsiattuto^ pmr aubio otntimmtr^ 



-12-0 C. 

-12'^ C. 
*1V02C, 



loe BM an £leoti*olyte. 

^^gS^zed by UOOgle 



Profs. Ayrton and Peny on Tee as an Electrolyte. 43 

the real facts. The opinion of M. Lorenz, that the great dif- 
ference between the results foand by MM. W. Weber, F. Kohl- 
ransch, and the physicists of the British Resistance Committee 
was the consequence of our imperfect knowledge of the laws 
of such induced currents^ finds no confirmation at all in the 
above experiments. 

(2) Absolute measurements of resistance can, with the 
means of galvanic observations nowadays at our disposal, be 
carried out with such exactness and certainty as can only be 
attained in few departments of physics. The notion widely 
accepted among physicists, that absolute measurements of resist- 
ance belong to those physical measurements which are capable 
of giving only roughly approximate values, and require pecu- 
liarly equipped localities lor carrying them out — ^an opinion 
to which W. Siemens, among others, has given expression in 
the sentence, "we may certainly pronounce positively that 
even the most practised physicists, supplied with the most 
perfect instruments and localities^ will not be able to make 
absolute resistance-measurements that would not differ by 
some percentage " — is refuted by the above results of experi- 
ment. According to my experience, these measurements can 
be effected with tolerable accuracy with very small means and 
in moderately equipped localities. 

[To be continued.] 



V. Ice as an I^lectrolyte. — Second Communication, By W. 
E. Ayrton and John Perry, Professors in the Imperial 
College of Engineering y TokiOy Japan*. 
[Plate n.] 

IN our former paper on Ice as an Electrolyte, read before 
the Physical Society on May 26th of this year, we de- 
scribed experiments which proved, among other things, that 
as the temperature of ice is allowed to gradually rise the con- 
ductivity increases regularly, and that there is no sudden 
change in passing from the solid to the liquid state. We also 

determined roughly the specific inductive capaciiy of < _.^^j. |- 

at —13^-5 0. and at +8°-7C.,and found that at the latter 
temperature it was about 2240 times as great as in the former. 
Preliminary experiments also showed us that there was very 
little change in the specific inductive capacity up to 0° C; and 
it was anticipated that there would not be a very great change 
after 0^ ; we therefore concluded that a very great change must 

• Communicated by the Physical Society. 

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44 Profs. Ayrton and Peny on Ice as an Electrolyte. 

occur at the melting-point. A series of farther experiments 
made with the same apparatas^ since the writing of the previous 
aper, have enabled us to draw approximate curves (rl. II.), 

A B 0, D E for the specific capacity of | ^^^^r }^^^"^~ ^^""'^ 
C. to +5° C, all tests of capacity being made by charging 
for ten seconds and then short-circuiting the -J ^r«4j«« r <5on- 

denser for fifteen seconds. From these it will be seen that, 
although the change at the melting-point is not quite as sudden 
as we expected, our anticipations are on the whole realized. 
It must be remembered too (see the description of the appa- 
ratus in our former paper) that, as the present experiments 
were made with a gradually rising temperature, the thermo- 
meter will always indicate a temperature a little higher than 
that of the ice ; the curve B C ought probably, therefore, to 
be even more vertical than it is. 

Distances measured perpendicularly to YOY represent 
temperature — ^positive temperature if measured to the right, and 
negative if measured to the left. Distances measured perpen- 
dicularly to X X represent specific capacity per cubic centi- 
metre for points on the dotted lines, and conductivity for points 
on the continuous lines. The scale for temperature is the same 
for all the curves. The scale for vertical distances for the 
capaciiy-curve D E is one eighth of that for the capacity- 
curve ABO; and the scale for vertical distances for the con- 
ductivity-curve J K is three thousandths of that for the curve 
FGH. 

The point A corresponds with a capacity per cubic cen- 
timetre of about 0'002 microfarad, at —12° 0. ; E corre- 
sponds with a capacity per cubic centimetre of about 0*1185 
microfarad, at + 5° C. ; at this apparent temperature the capa- 
city was increasing so rapidly as to make exact measurements 
very difficult, although the temperature was increasing but 
slowly. The point F corresponds with a specific resistance 
per cubic centimetre of about 2240 megohms, at — 12°*4 C. ; 
and K with a resistance per cubic centimetre of about 0*34 
megohm, at + 1 1°'02 C. As in our previous experiments, the 
water employed in the water-condenser was distilled, and the 
ice was formed by freezing it with an external freezing-mixture 
no particle of which was allowed to fall into the distilled 
water. 

The important theory which Prof. Clerk Maxwell has deve- 
loped, by comparing the propagation of electro-magnetic dis- 
turbances through the ether with the propagation of light-vi- 
brations, has been illustrated only by paraffin (a non-conductor); 

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Dr. J. Croll on Le Sage's Theory of Gravitation. 45 

and he has not considered the propagation of electro-magnetic 
disturbances in a conducting medium. Bat according to a 
former paper of ours, on the " Viscosity of Dielectrics," no 
dielectric can be assumed to be non-conducting, and the 
charging of any condenser whatever is always accompanied 
with absorption phenomena ; also absorption certainly increases 
with conductivity. 

Hence although, if a method of experimenting were employed 
in which a water-condenser of great internal resistance were 
discharged through wires of less and less resistance for shorter 
and shorter periods of time, the measured specific inductive 
capacity might get less and less, and gradually approach a 
valne equal to the square of the index of refraction of water 
for infinitely long luminous waves (the index of refraction for 
air being called unity), still practically the measured specific 
inductive capacity can never be even approximately equal to 
the refractive index of water, since the absorbed charge is 
immeasurably greater than the surface-charge. We therefore 
need not expect to find the specific inductive capacity of water 
in its variations with temperature consistent with Dr. Glad- 
stone's results for index of refraction. When Prof. Clerk 
Maxwell takes into account conductivity, his equations are not 
generally integrable ; but even if they were they could not deal 
with the real case, because he leaves absorption quite out of 
account. 

Joly 30, 3877. 

VI. Le Sage's Theory of Gravitation. 
By Jambs Croll, LL.D., F.R.S* 

LE SAGE^S theory of gravitation is at present exciting a 
good deal of attention among physicists. This is per- 
haps to a considerable extent owing to the fact that some of 
the conditions arbitrarily assumed by Le Sage in his hypo- 
thesis have been proved, from the kinetic theory of gases, to 
follow as necessary consequences. 

A clear and able account of this theory has been given by 
Mr. Preston in the Philosophical Magazine for September and 
November last. Mr. Preston has endeavoured to answer all 
the objections which have been urged against the theory f. 
There is one objection, however, which appears to me not to 

• Commonicated by the Author. 

t Mr. W. B. Taylor,: in an interesting article on Kinetic Theories of 
Gisritation, published in the Smithsonian Report for 1876, lays down 
six fundamental characteristics of gravitation, with which every theory, he 
says, must agree. Of these six requirements, Le Sago's theory, he main- 
tuns, satisfies but two — namely (1) that the direction of gravity is radial 



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46 Dr. J. OroU on Le Sage's Theory of Gravitation. 

have been fully met. It is a necessary condition of Le Sage's 
theory, in ocier that gravity inay be proportional to mass^ 
that the total volume of the free spaces in a substance in the 
form of interstices between the molecules must be great com- 
pared with the total volume of matter contained in the mole- 
cules themselves. This condition of free interstices Mr. Preston 
considers to be satisfied by assuming the molecules to be small 
relative to their mean distances. 

Were we at liberty to make any assumptions we choose in 
reference to the smallness of the molecules of matter and their 
distance apart, we might be able to satisfy the conditions of 
Le Sage's theorv as to mass ; but this we are not at liberty to 
do. Modem pnysics has enabled us to determine, at least 
roughly, the size of the ultimate molecules of matter and also 
their distance apart. This subject has recently been investi- 

Sted by Sir W illiam Thomson, the details of which will be 
md in a remarkable paper in * Nature,' vol. i. p. 551. Sir 
William says the diameter of the molecule cannot be less than 
500.000.000 ^^ ^ centimetre. The number of molecules in a 
cubic centimetre of a liquid or a solid may, he says, be from 
3 X 10^ to 3 X 10^. This gives the distance from centre to 
centre of two consecutive molecules to be from |^ to 

46070 0.0 00 ^^ * centimetre. Now, if we take the mean of 
Sxese two values, we have -.. ^^^„^-- of a centimetre for the 
distance between the centres. The mean spaces between the 
molecules are therefore less than the diameter of the molecules 
themselves. Under this condition of things, it must be abso- 
lutely impossible that a gravific particle, even though it were 
infinitely small, could penetrate to the extent of a thousandth 
part of a centimetre into the interior of a body without having 
its motion stopped by coming into collision with a molecule. 
Le Sage's theory appears therefore to be utterly irreconci- 
lable with Sir William's conclusions regarding the size of the 
material molecule. But even supposing we were to assume, 
what we are hardly warranted to do, that the molecules are 
10,000 times smaller, and their distance apart 10,000 times 
greater than Sir William Thomson concludes, still this would 
not assist the theory. The gravific particles would then, no 
doubt, penetrate a little further into the interior of a body ; 
but beyond a few feet, or perhaps a few inches, no particle 
could go. 

towards the acting mass, and (2) that its intensity diminishes as the square 
of the distance. But some of Mr. Ta^lor*s objections have already been met 
by Mr. Preston in his memoir ; beside, one or two of Mr. Taylor's funda- 
mental postulates seem doubtf^oL 



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[ 47 ] 

VII. On the Artificial Production of Corundum, Ruby^ and 
various Crystallized SUieates. By MM. E. Frbht and Feil*. 

SYNTHETIC mineralogy (that is to say, the artificial pro- 
d action of minerals) presents, in a scientific point of view, 
an interest which every one can understand ; for it throws the 
greatest light opon the mode in which minerals are formed, 
and permits ns to solve certain questions, relative to their com- 
position, which chemical analysis often leavea undecided. In 
fact, a mineral which appears most pure contains almost always 
foreign substances interposed which existed in the medium 
that formed it ; analysis is then {)owerless to determine the 
real composition of the mineral, while a synthetic reproduction 
enables us to distinguish the constituent elements from those 
which are merely accidental. 

A great number of minerals have been artificially produced 
in the dry way, in the wet way, and by M. Becquerel's inge- 
nious methods ; and synthetic reproduction is daily receiving 
some fresh extension^ as is proved by the recent discoveries of 
M. Hautefeuille. 

Corundum has, perhaps, more than any other mineral ex- 
ercised the sagacity of chemists. The excellent investigations 
on the difierent modes of crystallization of alumina whicn have 
been published by Ebelmen, de Senarmont, and since by 
MM. H. Sainte-Claire Deville and Caron, by M. Graudin, and 
by M. Debrayt, are known to every man of science. Even 
after these remarkable researches, however, we have thought 
we might still be permitted to interest the Academy by making 
known the processes we employ for the production of differ- 
ently coloured and crj'stallized alumina (that is to say, ruby' 
and sapphire) in masses sufficiently large to be used in horo- 
logy ana to be cut by the lapidary. It will probably be pos- 
sible to apply the methods we are about to describe to the 
artificial proauction of other minerals ; in this respect they 
seem to possess a true scientific interest. 

Wishing to approximate as nearly as possible to the natural 
conditions which have probably determined the formation of 
corundum, ruby, and sapphire, we have borrowed from industry 
its most energetic heat-producing appliances, which permit an 
elevated temperature to be producea, to be maintained for a 
long time, and considerable masses to be operated on ; indeed 

« Traiifllated from the Comjries Heneku de TAeadhnie d$B Soieneei, Dec. 5, 
1877, tome Ixxxv. ppw 1029-1036. 

t It is known that, by treating heated phosphate of alumina and lime 
with chlorh^dric add, M. Debray has obtainea at the aame time apatite 
and cfyvtallized alamina. 



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48 MM. Fremj and Feil on tlie Artificial Production of 

we have often acted on 20 or 30 kilograms of material, which 
we kept heated nninterruptedly for twenty days. 

It was in the oven of Feil s works that we conducted the 
experiments which required the highest temperature. When 
our trials demanded prolonged calcination, we had recourse to 
a glass-furnace whicn was generously placed at our disposal 
by the Company of Saint-Gooain. In this case our essays were 
directed by an eminent chemist, M. Henrivaux, whose intelli- 
gent supervision secured their success, for which we here render 
him all our thanks. 

The following is the method which permitted us to produce 
the largest quantitv of crystallized alumina : — 

We commence by forming a fusible aluminate, and then 
heat it to bright redness with a siliceous substance. In this 
case the alumina is slowly separated from its saline combination 
in presence of a flux, and cr;y^stallizes. 

We attribute the crystallization of the alumina to various 
causes : — either the volatilization of the base with which the 
alumina is united ; or the reduction of this base by the cases 
of the furnace ; or the formation of a fusible silicate which, by 
the combination of its silica with the base, isolates the alumina ; 
or, finally, a phenomenon of liquidation which produces a very 
fusible silicate and some hardly fusible alumina. All these 
cases presented themselves in our essays ; but the displacement 
of alumina by silica appears to us the surest process for effect- 
ing its crystallization. 

Beveral fusible aluminates lend themselves to these different 
kinds of decomposition ; that which, up to the present, has 
given us the neatest results is the aluminate of lead. When 
A mixture of equal weights of alumina and minium is placed 
in a crucible of fire-clay, and calcined at a bright-red heat for 
a sufficient time, two different layers are found in the crucible 
after cooling : the one is vitreous, and formed chiefly of silicate 
of lead ; the other is crystalline, often presenting geodes filled 
with beautiful crystals of alumina. In this operation the sides 
of the crucible act by the silica which they contain. They 
are always made thinner, and often perforated, by the action 
of the lead-oxide ; therefore, to avoia loss of the product, we 
usually conduct the operation in a double crucible. 

The experiment just described gives white crystals of co- 
rundum ; when we would obtain crystals presenting the rose- 
colour of the ruby, we add from 2 to 3 per cent, of bichromate 
of potass to the mixture of alumina and minium. The blue 
coloration of sapphire is produced by employing a small 
quantity of oxide of cobalt mixed with a trace of bichromate 
of potass. The ruby crystals thus obtained are ordinarily 



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Corundum^ Rubt/, and various Crystallized Silicates. 49 

coated with silicate of lead, which we remove in yarions ways — 
either by the action of fnsed oxide of lead, or by fluorhydrio 
acid, or by potass in fusion, or by prolonged calcination in 
hydrogen, and afterwards by the action of alkalies and acids ; 
but in certain cases we find in the geodes some nearly pure 
crystals, which then exhibit all the characters of the natural 
oonindums and rubies — possessing their composition, adaman- 
tine brilliance, hardness, specific gravity, and crystalline form. 

Our rubies, in fact, scratch quartz and topaz ; their specific 
gravity is 4*()-4'l. They lose, like natural rubies, their rose- 
ooloar when strongly heated, and resume it on cooling. Sub- 
mitted to lapidaries, they have been found as hard as, and often 
harder than, natural ones. They rapidly wear away the best 
grindstones of hardened steel. M. Jannettaz has kindly sub- 
mitted our rubies to crystallographic observations ; with the 
Amici microscope they present a black cross in their interior 
and coloured rings upon the margins. 

The crystals wnich we have had cut, and now exhibit to the 
Academy, have not yet the brilliance demanded by commerce, 
because they did not present to the lapidary faces favourable 
for cleavage and cutting ; but here are some crystalline masses 
weighing several kilograms, among which we shall doubtless 
find some that can be easily cut. 

We will now describe the method which has enabled us to 

Erodace the fine specimens of crystallized silicates which we 
ly before the Academy. The experiments about to be de-. 
scribed are connected with the preceding ; for they have fre- 
quently given us crystals of corundum together with crystallized 
nlicates. 

It was by means of fluorides that we produced the crystal- 
lized bodies, of which we have still to speak. In carrying 
out these researches we have had the opportunity of apprecia- 
ting all the accuracy of the observations of M. Daubr^e, who 
first demonstrated the important part played by fluorine, as a 
mineraliaser, in the formation of mineral beds and of silicates. 
Ibose views are confirmed anew by our experiments. 

Guided by the classic writings of M. Henri Sainte-Claire 
Deville, we have ascertained that, of all the mineralizers, 
perhaps the most active is the fluoride of aluminium. * Sub- 
mitting a mixture of equal weights of silica and fluoride of 
aluminium to a red heat during several hours, we verified that 
by the mutual reaction of the two substances fluoride of 
diicium is liberated, and a crystallized body is obtained which 
appears to be kyanite — that is, silicate of alumina. According 
to the determinations of M. Jannettaz, this body occurs in 
doubly refracting acicular crystals which extinguish light 
PlUl. Mag. S. 5. Vol. 5. No.^28. Jan. 1878. E 

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50 MM. Fremy and Fell on the Artificial Production of 

obliquely with respect to their edges. Doubtless they belong 
to one oi the oblique systems— the oblique prism with rhombic 
base, or the doubly oblique prism. These crystals gave the 
following composition : — 

Silica 47-65 

Alumina 51*85 

Loss 0-50 

This comes near to the composition of natural kyanite*. 

The action of fluoride of aluminium on boric acid gave a 
crystallized borate of alumina which corresponds to kyanite. 
We are at present carrying out a series of trials in which 
fluoride of aluminium will act upon other mineral acids. 

The important fact of the volatility of the fluoride of alumi- 
nimu; discovered by M. Henri Sainte-Claire Deville, enables 
US readily to explain the remaining experiments. When a 
mixture of equal weights of alumina and fluoride of barium, 
into which has been introduced 2 or 3 per cent, of bichromate 
of potass, is heated to and maintained at a very high tempera- 
ture during a long time, a crystallized mass is obtained the 
study of which is of the greatest interest. If the calcination 
has been effected in a crucible covered with another (which 
serves in some sort as a condenser), two sorts of crystals are 
found in the crucibles : the one sort are long colourless prisms, 
often several centims. in length, and presenting the aspect of 
the silvery flowers of antimony ; the others are ruby crystals, 
remarkable for the regularity of their forms and beautiful 
rose-colour. 

The long prismatic colourless crystals are formed by a 
double silicate of baryta and alumina, which present the 
composition : — 

Silica 34-32 

Baryta 35-04 

Alumina 30-37 

In our essays this double silicate often crystallized in rather 
short, hard and transparent, clinorbombic prisms which, M. 
Terrell has ascertained, have the same composition as the long 
and hollow prismatic needles. 

M. Jannettaz has proved that the long prisms are often con- 
stituted by four plates with parallel faces, forming the faces of 
a hollow prism. These plates are very thin ; under the micro- 
scope they extinguish light ; or rather they let darkness persist 
between two Nicols, parallel to their mutual intersections ; the 
• The crystals we obtained are very easily produced, but are not of 
lanje size j they may therefore belong to those fibrous varieties of dysthene 
wnich have been described under the names of Fribolite, BucholEite, 
i»nihte, and Sillimanite. ^ 

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Corundum f Rubt/j cmd various Crystallized Silicates. 51 

plane of the optic axes is parallel to these intersections ; they 
cat one another at angles of 60"" 42' and 119^ 18^. 

There is therefore produced in this canons reaction comndum 
and a crystallized doable silicate. These two crystalline sub- 
stances result from the following transformations : — 

In the calcination of the mixture of alumina and fluoride of 
barium there are evidently formed fluoride of aluminium and 
baryta. The fluoride of aluminium, once produced, must have 
acted in two difibrent ways. Decomposed hy the gases from 
the hearth, it formed fluorhydric acid and corundum, which 
crystallized under the influence of the vapours. Acting be- 
siaes upon the silica of the crucible, it gave rise to silicate of 
alumina, which, combining with the baryta, produced the fine 
ciystals of double silicate of alumina and baryta which wo 
euiibit to the Academy. Such, in our opinion, is the theory 
of the reaction. 

Permit us now to dwell on the conditions which have de- 
termined the crystallization of the two substances, corundum 
and the double silicate. Looking at the specimens we here 
exhibit, and which present such well-defined crystals, one is 
strock with the place which they occupy in the crucibles : 
they seem to have been volatilized ; and yet we have ascertained, 
by exposing them to the highest temperatures of our furnaces, 
that tney are absolutely fixed. It is because the fluorides are 
not merely powerful mineralizera ; they are also compounds 
which, as was formerly said, give wings to the least-volatile 
substances. Do we not recollect, indeed, that remarkable 
formation of orthose felspar, produced artificially and found 
in the upper part of a copper-iumace at Mansfeld? The 
employment of fluoride of oiicium in the melting-bed of the 
famace which produced that felspar permits the belief that the 
fluorine intervened in that case as a transporting agent. It 
was evidently this which presented itself m our experiments, 
as in those which have been so often performed by M. H. 
Sainte-Claire Deville : the agents of the transport and crystal- 
lization of the corundum and the silicate were likewise the 
fluorine compounds which we employed. 

It was to be presumed that this action of fluoride of barium 
upon alumina in presence of silica, forming a crystallized double 
suicate, would reappear as a general phenomenon connected 
with the decomposition of the fluorides by diflerent bases. This 
we have, in fact, proved ; in another communication we will 
describe some crystallized double silicates produced under 
the same conditions as the double silicate of alumina and 
baryta ; and then we shall give the general formulaB of these 
oomponnds. 

E2 

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52 Mr. F. Field on a Variety of the Mineral Oronstedite. 

Such is the brief account of our researches which we wished 
to present to-day to the Academjr. It is probable tiiat our 
experiments, which give, in considerable masses, substances 
whose hardness is comparable to that of the natural ruby, will 
be utilized from time to time by the watchmaker, and even by 
the jeweller. We will say, in conclusion, that in this labour 
the aim we pursue is exclusively scientific ; consequently we 
put into the possession of the public the facts we have dis- 
covered, and shall be very happy to learn that they have found 
useful industrial applications. 

VIII. OnaVariety of the Mineral Oronstedite. By Frederick 
Field, FM.S., Vice-President of the Chemical Society*. 

THE various analvses of the interesting mineral Oronstedite, 
named after tke Swedish mineralogist Cronstedt and 
hitherto found only in two localities (Przibram in Bohemia and 
Wheal Maudlin in Cornwall), are rather conflicting, since the 
amounts of ferrous and ferric oxide differ considerably, as the 
following results will show. Nevertheless all examinations 
tend to prove that Oronstedite is essentially a hydrous silicate 
of ferrous and ferric oxide. 

From four specimens from Przibram we have: — 

Silicic acid 22-452 

Ferric oxide 

Ferrous oxide 58*852 

Manganous oxide 5*078 

Magnesium oxide 2*885 

Water 10*700 

99*967 

This was corrected by Von Kobell, after a determination of 
the degree of the oxidation of the iron, which gave: — 

Silicic acid 22*452 

Ferric oxide 35*350 

Ferrous oxide 27*112 

Manganous oxide 5*078 

Mangnesium oxide 2*885 

Water 10*700 

103*577 

And in two more analyses, one by Steinmann and one by 
Damour, the ferrous oxide varied more than 2 per cent.:— 

• Communicated by the Author. 



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Mr. F. Field on a Variety of the Mineral Cronstedite. 53 

SiO,. FeaO,. FeO. MnO. MgO. H,0. 
Steinmann... 22-83 29-08 31-44 3-43 325 10-70 

Damour 2139 2908 33-52 I'Ol 402 9-76 

Messrs. Maskelyne and Flighty in a valuable paper upon 
certain Cornish and other minerals (vide * Jonmal of the Che- 
mical Society/ new series, vol. ix. p. 9), gave the results of 
some analyses of specimens of Cronstedite from Cornwall, 
handed them by Mr, Tailing ; but these, again, are not very 
concordant. 
The first analysis of this mineral gave the following num- 

!»"•— Iron protoxide 36-307 

Iron peroxide 36-762 

Silicic acid 17-468 

Water 10-087 

Calcium oxide *087 

100-711 
A second analysis, with a fresh and more carefully selected 
material, gave the following percentages : — 

Iron protoxide 88-570 

Iron peroxide 32-752 

Silicic acid 18-546 

Water 10-132 

100-000 
Mr. Tailing called my attention to an amorphous, dark leek- 
green mineral, at times associated with Cronstedite, which 
struck me as interesting, inasmuch as, although differing so 
widely at first sight from the brilliant black of the latter, yet 
had exactly the appearance and colour of the streak of Cron- 
stedite after abrasion with a file or some hard mineral. 

Qualitative examination proved it to consist entirely of fer- 
ric and ferrous oxides, silicic acid, and water. Its specific 
gravity was 3, hardness about 2*5. On heating, water was 
evolved, and the green powder rapidly passed into yellowish 
brown. No traces of eitner magnesium- or manganic oxide 
could be detected (as in the case of the Bohemian mineral) ; 
and there was no evolution of carbonic acid on the addition of 
weak hydrochloric acid, by which it is instantly decomposed 
with separation of silica and solution of the two iron oxiaes. 
A quantitative analysis yielded: — 

Ferrous oxide 39*46 

Ferric oxide 18*51 

Silicic acid 31-72 

Water 11-02 

100-71 



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54 Prof. Cayley on the Distribution of Electricity 

It would be useless perhaps to attempt to give a formula to 
the above ; and the entire absence of crystallization deprives it 
of much of the interest it should otherwise possess. 

The following, perhaps, would give the best idea of its con- 
stitution : — 

3 (FeO, SiO, H, 0) + Fe, O3. 

Found. Calculated. 

Ferrous oxide 39-46 40-74 

Ferric oxide 18-51 1509 

Silicic acid 31-72 33-96 

Water 11-02 10-18 

100-71 99-97 

It may be merely a coincidence ; but it is worthy of remark 
that the water in the mineral just described and that in tho 
Cronstedite examined by Messrs. Maskelyne and Flight* is 
much about the same, which can also be said of the ferrous 
oxide, neither of them varying 1 per cent., while the silicic 
acid and ferric oxide seem, so to speak, to have changed places. 

Cronstedite. Green mineral. 

Silicic acid 18-546 31-72 

Ferric oxide 32-752 18-51 

51-298 50-23 

. It has already been remarked that, on heating the green 
mineral, its colour is changed to yellowish brown; and on ex- 
amination of the residue, no trace of ferrous oxide could be 
detected. When the water has been drawn off, at the lowest 
possible temperature, and the mineral further heated, it rapidly 
gains in weight from absorption of oxygen. 



I 



IX. On the Distribution of Electricity on two Spherical 
Surfaces. By Prof. Cayley f. 

N the two memoirs " Bur la Distribution de ^Electricity k 
la Surface des Corps Conducteurs," Jf<^/t. deVInst. 1811, 
Poisson considers the question of the distribution of electri- 
city upon two spheres : viz. if the radii be a, 6, and the dis- 
tance of the centres be c (where c>a + A, ihe spheres being 
exterior to each other), and the potentials within the two 
spheres respectively have the constant values h and g, then — 

for Poisson's /(^Writing 0(.r), and for his F^^j writing 



* From the moat carefully selected specimen. 
t Commimicated by the Author. 



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on ttoo Spherical Surfaces. 55 

4(j?) — the question depends on the solution of the functional 
equations 

where of course the a of either equation maj be replaced by a 
different variable. 

It is proper to consider the meaning of these equations : for 
a point on the axis, at the distance x from the centre of the 
firet sphere^ or say from the point A, the potential of the 

electricity on this spherical surface is cw^^ or — <^( — ), accord- 

*C \ ill? / 

ing as the point is interior or exterior ; and, similarly, if a 
now denote the distance from the centre of the second sphere 
(or, say, from ^e point 5), then the potential of the electricity 

on this spherical surface is b^x or — <!>( — ), according as the 

point is interior or exterior ; <^(^^ is thus the same function 
of (a, Oy b) that ^{a) is of (xy b, a). Hence, first, for a point 
interior to the sphere A, if a; denote the distance from A^ and 
therefore c—x the distance of the same point from B, the 
potential of Hie point in question is 



^a^x+ <I>( 1; 



and^ secondly, for a point interior to the sphere B, if ^ denote 
the distance from B and therefore c—x the distance of the 
same point from A, the potential of the point is 



= ^Kc-^.)-^^(->' 



The two equations thus express that the potentials of a point 
interior to A and of a point interior to B are = h and g re- 
spectively. 

It is to be added that the potential of an exterior point, dis- 
tances from the points A and B =a? and c-^x respectively^ ia 



x^\x/ c^x \c— ^/ 



and that by the known properties of Legendre's coefficients, 
when the potential upon an axial point is given, it is possible 
to pass at once to the expression for the potential of a point 
not on the axis, and also to the expression for the electrical 
density at a point on the two spherical surfaces respectively. 



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56 Prof. Oayley on the Distribution of Electricity 

The determination of the fanetions ^{x) and ^{x) gives tbns 
the complete solution of the question. 

I obtain Poisson's solution bj a different process as fol- 
lows : — Consider the two functions 

aHc—a) aj? + b 

and 

b\c—x) «a?+/8 

and let the nth functions be 

5=^ and ""^-^f 

lespectively. 

Observing that the valnes of the coefficients are 

(a, b )-( -a», a'e ), and («, /8)=(-6», Ve ), 
|c, d| ]-e,c'-b»\ 17, 8 1 |-c,c»-a»| 

SO that we have 

a + d=« + S, =(?-a'-ft», ad— bc=aS-/37, =saV, 

and consequently that the two equations 

(X+iy ^ (a-hd)» (X+iy ^(« + 8)» 
X *ad-bc' \ «S-)87 

are in fact one and the same equation 

for the determination of X, then (by a theorem which I have 
recently obtained) we have the following eqaations for the 
coefficients 

(a^, b«), (««, /3,) 

|c„, d,| |7„ Bn\ 
of the nth functions; viz. these are: — 

"^■^^"^ jra(j^)"'{(^"*'-l)(a*+b) + (\--X)(-d;t+ 
c.«+d.= „ „ {(X»+'-l)(ca;+d) + (X--X)( cx- 

and similarly 

««*+^.= j;5^(j^)""'{(\-+'-l)(*r+/3) + (\--X)(_&r+ 
7^+S,= „ „ {(x-+'-l)(7j.+S) + (x«_x)( y,- 



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on two Spherical Surfaces. 57 

Observe that iihese equations give, as thej onght to do, 
ao«+bo=^, c^-|-dQ=l, aia?+bi=aa? + b, Ci« + di=cd?4-cl; 
and similarly 

a' 
Sobstitating in the first two equations in place of jt, 

and in the second two equations — — in place of 4^/ we obtain 




yi^ + fii.(c— -a?)=^(ai,+i« + b«+,), 

the last two of which are obtained from the first two by a mere 
interchange of letters ; it will therefore be sufficient to prove 
the first and second equations. 
For the first equation we have 

a^ + b,(.-ar)= ^fi±^)"" KX->-l)[aa' + b(c-^)] 

-|-(X«-X)[-da»+b(c-^)]}, 
where the term in { } is = 

viz. this is 

=:a'{(X»+'-l)(c»-a»-jC^) + (X»-X)(i»-c^)}; 
or it is 

=a'{(X-+'-l)(7^+S) +(X--X)(y^-«)}, 

whence the relation in question. 

The proof of the second equation is a little more compli- 
cated : we have 

+(X--X)[co»-a(c-«)]} 
where the term in { } is s 

(X-+«_l)[_ca»+ (c»-t»)(c-ar)] + (X»-X)[-ca« + a'(c-a]. 

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58 Prof. Cayley on the Distribution Q/Eleetridty 

Comparing this wiih 

(X-*'-X)(-&r+/9)}, 
where the term in ^ [is 

it is to be observed that the quotient of the two terms in { {- 
is in fact a constant ; this is most easily verified as follows. 
Dividing the first of them by the second we have a quotient 
which when ^=:c is 

(X*-*-'-l)(^ca») + (X''^X)(^m') ^ a^(x*-^'-l-f.x'^X) 

__^(X + li_. 

and when jr=0 is 

(X*-^'->l)c(c»^a«-y) _ (x*^*-l)(c»^a»-y) 

(X«+»-1)6-^c + (X*+'-X)JV "" (X*+"-l+X*-''-X)6' 

6^(X + 1) ■• 

these two values are equal by virtue of the equation which de- 
fines X ; and hence the quotient of the two linear functions 
having equal values for ^=c and 4r=0, has always the same 

value ; say it is = kVxA-Y\ ' Hence, observing that a + d = 
« + S, =c^— a'— A'*, the quotient, Cn(^-\-dn{c—x) divided by 

_ X-fl c'-a^^b^ _ 1 

or we have the required equation 

Considering now the functional equations, suppose for the 
moment that ^ is s=0 ; the two equations may be satisfied bv 
assuming ^ 



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an two Spherical Surfaces. 59 

We in fact^ from the foregoing* relations^ at once obtain 

* = -A^ — — y^ + — rr *'* rM. 

To satisfy the first equation we must have M sgL ; viz., this 
being so, the equation becomes 

or, since (v? + ^=l; the equation will be satisfied if only 
aL=:l, whence also M=l- And the second equation will be 

satisfied if only — =6M ; viz., substituting for L, M their 

value, we find G)=a5. 

Supposing, in like manner, that AasO, ^ retaining its 
proper value, we find a like solution for the two equations ; 
and by simply adding the solutions thus obtained, we have a 
solution of tlie original two equations 



c 
viz. the solution is 



i*G-fJ+*^(^)=^' 



We have a general solution containing an arbitrary constant 
P by adding to the foregoing values 

for <f>x a term P&(g— 6) 

s/c?{c'-x)-'a{i?'-b^ — ex) 
and for ^x a term 

Pa(&~ a) 

V6^(c— A')— «(c^— g'— c^)' 

as may be easily verified if we observe that the function 
c?{c^x)'^x{(?^V^cx)y 

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60 DistrihtUion of Electricity on two Spherical Surfaces. 
writing therein for «, becomes 

and similarly that ' 

writing therein ^ for Xy becomes 

More generally, the terms to be added are for ^x a term as 
above, where r denotes a function of x which remains unal- 

tered where x is changed into ., ^,j> — '—. and for ^x a term 

as above with P' instead of P, where P' denptes what P be- 

comes when x is changed into . But these additional 

c^^x 

terms vanish for the electrical problem, and the correct values 

ot d)x, ^x are the particular vsuues given above. 

It is to be remarked that the function 

a\c—x) , _ g' 

c^x 
viz., considering x as the distance of a point X from A, then 
taking the ima^e of X in regard to the sphere B, and again 
the image of this image in regard to the sphere A, ihe function 
in question is the distance of this second image from A. And 
similarly the function 

b^(c-x) . y 

-3 « IS — « — 5 

(T—a^'-cx a' 

c-^x 

viz., considering here ^ as the distance of the point X from B, 
then taking the image of X in regard to the sphere A, and 
again the image of niis image in regard to the sphere B, the 
function in question is the distance of this second image from 
B. It thus appears that Poisson's solution depends upon the 
successive images of X in regard to the spheres B and A alter- 
nately, and also on the successive images of X in regard to 
the spheres A and B alternately. This method of images is 
in fact employed in Sir W. Thomson's paper " On the Mutual 
Attraction or Bepulsion between two Electrified Spherical 
Conductors," Phil. Mag., April and August 1853. 



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[ 61 ] 

X* On the Destruction of the undeveloped Pliotographie Image^ 
By Captain Abnby, R.E.y F.R.S.* 

IT has always seemed that more experiments were required 
in regard to the destruction of the undeveloped photo- 
graphic image by chemical or physical agency. In the pre- 
sent communication I propose to give some instances of the 
destruction by the former, as it appears they may be capable 
of throwing light on some of the phenomena which have as 
yet been only imperfectly explained. 

The undeveloped Da^aerrean image, as is well known, can 
be destroyed by the action of iodine, bromine, or chlorine on 
the sensitized surface of the plate ; and it can also be destroyed 
by oilier agents which might naturally be expected to do so. 
Perhaps the most remarkable method of destroying the image, 
however, is by the action of the rays lying at the least-refran- 
gible end of uie spectrum. Draper and others have applied 
wis to obtain an image of this portion of the solar spectrum 
by submitting a plate to which had been given a preliminary 
exposure to its action. On development with mercury, a ne- 
gative picture of the red end of the spectrum was obtained, 
together with a positive picture of the violet end. 

W ith iodide of silver formed in a film of collodion, the image 
is known to be destroyed by potassium iodide, probably be- 
cause it forms a definite compound with the silver image. 
Sulphuretted hydrogen, coal-^as, and other similar bodies also 
destroyed the image, by causing a reduction of silver all over 
the film. This last phenomenon scarcely need be considered 
here, as it is chiefly dependent on the silver nitrate which 
kept on the film for sensitizing-purposes. 

Very few, if any, experiments are recorded on the destruction 
of the image on silver bromide, principally, it may be pre- 
sumed, because the use of that sensitive salt of silver has only 
become general within the last few years. The practical pho- 
tographer well knows the great difficulties that are met with 
in sensitizing an entirely oromized collodion in the silver- 
nitrate bath ; and until the emulsion process was introduced 
in a practical form, experimenting with silver bromide to any 
great extent was an unsatisfactory undertaking. 

In what is known as the ^^ washed collodio-bromide emul- 
sion process " we are now able to prepare films containing 
silver bromide in which neither soluble bromide nor yet silver 
niirate are in excess, and experimenting is more easily per- 
formed even than with silver iodide. 

There has always, however, been one drawback to this pro- 

« Communicated by the Author. 



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62 On tlie Destruction of the undeveloped Plu>tographic Image. 

oess ; and that is^ the danger of making emulsified silver bro* 
mide which should give a veiled image. Varioas means of over- 
coming this difficulty have from time to time been employed ; 
and it was in my endeavoiur to discover the reason wny they 
were effective that I was led to make other experiments^ 

Now the veil for fog, as it is more commonly designated) 
seemed to depena on similar chemical changes in the bromide 
film to those on which the existence of the image itself de- 
pended. Byfinding out the cause of one^ it seemed probable 
that the reason of me other might be discovered. 

It wafl found, if films made by the silver-bromide emulsion, 
which on development gave an unveiled image, were exposed 
to light and then treated with (1) bromine, (2) iodine, (3) 
nitric acid, (4) sulphuric acid, (5) cupric bromide, (6) ferric 
chloride, and other similar bromides and chlorides which 
easily part with a portion of their bromine or chlorine to 
metallic silver, that on development no trace of the action of 
light need be apparent. If we suppose that the photographic 
image is dependent on the reduction of the argentic to a state 
of argentous bromide, the action of (1), (2), (5), and (6) would 
be easily accounted for : (1) and (2) would furnish one of the 
atoms (which, for convenience sake, I will call the looee atorn) 
of silver with the necessary atoms to saturate it. Thus i-^ 
2Ag,Br + 2I=sAg,Br8+Ag,I,. 

Similarly, by a decomposition of cupric bromide or the 
ferric chloride, the same reaction would be obtained: — 
2 Ag, Br + 2 Cu Br,= 2 Ag, Br, + 2 CuBr. 

The action of nitric acid and sulphuric acid was more 
difficult of explanation, unless it were believed that one 
atom of the argentous bromide was completely removed. 
When testing silver-iodide films with these bodies, it was 
found that nitric acid did not destroy the image, but that 
it could be developed after its application. This experiment 
seems to prove that the ima^e on the iodide was not caused 
by a separation of metallic suver. The question then arose as 
to wheuier these images were formed by argentous iodide at 
all, in which case it might be considered that the chemical 
theory failed. In order to obtain more evidence, it was thought 
advisable to try whether the loose atom of silver, if it existed, 
could be oxidized. K this could be effected, it seemed pro* 
bable that the image would be undevelopable. 

Silver bromide was first put to the test. Plates 'wore treated 
with potassium bichromate, potassium permanganate, or with 
chromic acid. In every case the image was obUterated and the 
film was in a state to receive another developable impression. 



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Notices respeeting New Boohs. 69 

The image on silver iodide was amenable to the last two oiudi- 
ling aeents, bat apparentij not to the first one. 

A sOyer-bromide plate, after the image had been oxidized^ 
was allowed to come into contact with nascent hydrogen ; and 
a partial restoration of the image was obtained^ bnt the distinct- 
ness was much marred by the reducing action that took place 
on the silver bromide which had received no impression by 
light. 

As a crucial test, however, both bromide and iodide films 
were exposed moistened to the action of ozone obtained by the 
ordinary electrical arrangements from perfectly pure oxygen ; 
and in all cases the image was totally destroyed. Whilst the 
film was still in the ozonized condition, it was again exposed, 
and a feeble image, due to the new exposure, was developable, 
whilst after destroying the ozone, a new exposure gave a vigo- 
rous picture. 

From these experiments are to be deduced that the image 
formed in the silver iodide is of the same nature as that formed 
in the silver bromide, the dijfference between them being pro- 
bably that in the former the atoms are more strongly bonded 
tlian in the latter, that oxidation of the loose atom of silver 
makes the image undevelopable, and that to this cause the 
deterioration of the image on dry plates by keeping after ex- 
posure is most probably due. If the red rays promote oxida- 
tion, as has recently been asserted by Chastaing, the pheno- 
mena observed by Draper and others, already alluded to, may 
be readily accounted for. 

XI. Notices respecting New Books. 

Bepori on the Administration of ike Meteorologieal D^artment of 

India^ in 1876-76* Goremment Central Press. 
Beport Off ^ Meteorology of India in 1875. By Henby F. 

BiiAirFoan, Meteorologieal Reporter to the Govenwnent of India. 

Ymt Tear. Calcutta, 1877. 

n^HB first of the above-named publications deals principally with 
the official establishment by the Government of India of the 
Meteorological Department on the 27th of September, 1875, sanc- 
tioning a scheme of reorganization recommended in the author's 
Beport of the 26th of July, 1875. To this report the author's name 
IS not appended ; but, from a remark on the publications of the De- 
partment, we believe it to be the production of Henry F. Blanford, 
Uie Meteorological Eeporter to the Government of India. To this 
report of the administration of the Department are appended some 
extracts from a report by Mr. F. Chambers, which contain some 
mteresting notices. It appears from these extracts that the first 
attempt at systematic Meteorological registration at Provincial 



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64 Notices respecting New Books. 

stations in the Bombay Presidency was made in 1861 — ^two years 
before the Brussels Conference, the outcome of which, among other- 
results, was the establishment of our own Meteorological Office 
under the direction of the late Admiral FitzBoy, and about four 
years after the general idea of systematic meteorological observa- 
tion, especially by officers in the army, navy, and mercantile marine, 
was suggested in this country. The observations in the Bombay 
Presidency were made in pursuance of orders received from the 
Honourable Court of Directors ; but at most of the stations they were 
soon discontinued altogether, whilst at others they were continued 
in a very inefficient and negligent manner. Towards the end of 
1852 the receipt of five complete sets of verified instruments from 
Engbind revived in a measure the work of observation in India. 
Orders were given to erect them at Belgamn, Poena, Bombay, 
Deesa, and Kurrachee, and place them in charge of the Superin- 
tendent of the GK)vemment Observatory at Bombay, and the senior 
Medical Officers at the other stations,, with this comment : — ^^' We 
would hope that, from the zeal and energy of Medical Officers in 
charge of European hospitals and their love of science, the observa- 
tions may be made by themselves and their establishments, without 
entailing on the public any expense on this account." The zeal and 
energy of the medical officers and their love of science, however, 
seem not to have been equal to the occasion; for after vainly en- 
deavouring until the end of 1855 to carry out the orders they had 
received without entailing expense on the public, it was arranged 
at the direction of the Honourable Board that two European soldiers 
should be told ofE at each station to undertake the duty of making 
meteorological observations, on an allowance of 25 rupees per month 
for each observatory. The soldiers were sent to the Bombay Ob- 
servatory early in 1856 for a preparatory course of training, on the 
successful completion of which they were furnished with certificates 
of competency for performing the work. Soon after this time the 
real work of meteorological registration may be said to have com- 
menced so far as the observers were concerned; for the work from 
this time appears to have been carried on generally in a thorougl| 
and trustworthy manner. 

Turning to the administrative report, the first portion of which 
has reference to the machinery of the Meteorological Departments 
previous to the establishment of the Meteorological Department by 
the Government and the reorganization of the observations, we find 
there were eighty-four observatories in India and its Dependencies. 
In the scheme of reorganization, one of the most important points 
was a redistribution of the observatories, in effecting which it was 
proposed to group low-lying and elevated observatories in pairs, in 
order to throw light on the variations of the atmosphere in a vertical 
direction. The result of the reorganization has been the establish- 
ment of 95 observatories, viz. 3 first class, 21 second class, 71 third 
class, which, with 9 independent observatories furnishing data, 
make a tol^ of 104 meteorological observatories actively at work in 
India. 



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Notices respecting New Books. 65 

Under the head of Publications we find the results obtained by 
the Meteorological Department of India will be pablished in two 
serial forms — ^an ' Annual Report on the Meteorology of India,' 
and * Indian Meteorological Memoirs/ the part of which about to 
be issued will contain : — 

Ist. On the Winds of Calcutta. 

2nd. On the Climate and Meteorology of Kdsbghar and Ydrkdnd. 

3rd. On the Diurnal Variation of the Barometric Pressure at 
Kmla. 

The Beport on the Mete3rology of India is a folio of 386 pages, 
297 being occupied with tables of results obtained at 87 stations. 
These comprise Solar Eadiation, Terrestrial Eadiation, Air-tempera- 
ture, Atmospheric Pressure, Anemometry, Hygrometry, Cloud-pro- 
portion, and Eainfall. The second paragraph of the introductory 
portion of this Eeport indicates in so lucid a manner the connexion 
of Meteorology with Physical Geography, and is of itself sufficient 
to exhibit the spirit in which Mr. Blanf ord has undertaken the work, 
that we quote it in extenso : — 

** As a field for the advantageous study of Physical Meteorology, 
India stands pre-eminent — in virtue not only of the intensity and 
variety of the phenomena it presents, but also of their intimate 
localiaition in a circumscribed arena. Isolated on the north by the 
gigantic mountain-range, which presents an impassable obstacle to 
any interchange of the lower half of the atmosphere with that of 
the regions beyond, and bathed on two sides by an ocean which 
stretches away without a break to the margin of the Antarctic land, 
it affords an almost unique example of the contrasted conditions of 
Luid and wat^, of continent and ocean, of great extent, yet for the 
most part accessible and uncomplicated by influences of unknown 
origin and uncertain magnitude. At the same time situated half 
within and half without the tropics, its southern extremity traversed 
by the terrestrial equator of heat, and dominated during five months 
of the year by a vertical sun, it receives in its greatest intensity the 
solar heat which is the source of all meteorological action ; and yet 
again so vast is its extent, and so varied are the physico-geographical 
characteristics of its different parts, that it exhibits within itself at 
one and the same moment extreme examples of the most opposite 
effects of that energy in the parching heat of the Scindian deserts 
and the torrential rains of the Ghdts and of Eastern Bengal." 

It is thus vrith a view of unfolding the laws of the physical int-er- 
dcpendence of Meteorological phenomena with the geographical 
features of a country, that Mr. Blanford has undertaken and effec- 
tively carried out the duty intrusted to him. A considerable por- 
tion of the introductory matter of this first annual volume consists 
of a most interesting and valuable sketch of the Physical Geography 
of India and its Dependencies, followed by a description of the 
physical characteristics of the Meteorological stations. The author 
then enters upon a careful discussion of the observations obtained in 
lb75, under the heads above mentioned. 

We cannot take leave of this most interesting volume without 
Phil. Mag. S. 5- Vol. 5. No. 28. Jan. 1878. F 

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66 Notices respectinff New Books. 

feeling assured that a great meteorological work has been commenced 
in India with every prospect of its being carried on successfully, so 
that in a few years it will rank with the great American and 
Mauritius systems, the one gathering and disseminating meteoro- 
logical data over the JN'orth-American continent, the other working 
up the meteorology of the Indian Ocean most advantageously, for 
the benefit of the numerous vessels traversing its surface. We are 
not unmindful of the labours in this direction of Piddington, who 
effected for the Bay of Bengal and the China Sea what Meldrum 
has for the Indian Ocean ; and we look forward with confidence 
for some important and valuable contributions on the storms that 
visit the Bay of Bengal in future volumes of the ' Indian Meteoro- 
logical memoirs. Indeed the meteorology of India will not be com- 
plete without a risume of the storms which have visited India and 
the Laws dedudble from them ; and we are satisfied, from the 
Eeports before us, that India possesses men fully equal to the work. 

The Theory of Sound. By John "William Steutt, Baron BAYLSiaH, 
M,A.y F,R.S.<i formerly Fellow of Trinity College^ Cambridge, 
Vol. I. London : MacmiUan, and Go. (8vo. Pp. 326). 
This is the first volume of a work of great scientific importance. 
Its object is to supply the student with a complete view of the 
mathematical treatment of the subject ; to do for it in its present 
stage of development what was done for it as it stood forty years 
ago by Sir J. Herschel's " well-known article on Sound " in the 
* Encyclopaedia Metropolitana.' In the present volume the author 
does not get so far as to treat of Atmospheric vibrations. So ela- 
borate a treatment of the vibrations of other bodies, it might be 
thought, would turn the treatise into a general treatise on wave- 
motions ; its limits, however, are determined by a sort of common 
sense. But it will be best to let the author speak for himself on this 
subject. 

'' In the choice of topics to be dealt with in a work on Sound, 1 
have for the most part followed the example of my predecessors. 
To a great extent the theory of Sound, as commonly understood, 
covers the same ground as the theory of Vibrations in general ; but 
unless some limitation were admitted, the consideration of such 
subjects as the Tides, not to speak of Optics, would have to be in- 
cluded. As a general rule we shall confine ourselves to those 
classes of vibrations for which our ears afPord a ready-made and 
wonderfully sensitive instrument of investigation." (P. vi.) 

Of the ten Chapters comprised in the present volume, the first 
three are introductory. The^r«* gives a brief view of the leading 
facts concerning the propagation of Sound, and those relating to 
musical notes and tones ; the second treats of harmonic motions 
kinematically ; and the third discusses very fully the case of a 
vibrating body having one degree of freedom. The next two 
Chapters (the fourth and fifth) are devoted to the consideration of 
vibrating systems in gener^ ; the last five to the special systems of 
Strings, Bars, Membranes, and Plates. 



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Ifotices respecting New Books. 67 

For the purpose of giving some notion of the extent to which 
these subjects are treated, we will indicate briefly the contents of 
one chapter ; and for this purpose we will take the last, viz. that oq 
Vibrations of Plates — a plate being a thin solid '' of uniform iso- 
tropic material and constant thickness " (p. 293). The general 
expressions in the case of such a plate are first investigated for 
the potential energy of each unit of area, and for its variation 
from which the equation for the motion of the plate at any one 
point is found, and then the equations of condition arising from the 
state of its boundary, whether free, clamped, or supported. In 
subjects of this kind, however, the difEculty only begins when the 
general equations have been formed ; and aocordLagly the next step 
is to modify them to suit the case of a circular plate and to integrate 
them when thus modified. The results obtamed are compared — 
both in respect to the principal tones, and the nodal lines — with 
the results of observation ; and a sketch is given of the history of 
the problem. Two other cases are also discussed. The first is 
that of a rectangular plate whose edges are free (the case in which 
the edges are supported being but briefly noticed) ; but in this 
case the mathematical difficulties necessitate the supposition that 
^=0; u e. the lateral contraction is assumed to be evanescent 
in comparison with the longitudinal extension. The results ob- 
tained on this supposition as to nodal lines and principal tones are 
found to admit of pretty close comparison with observations on a 
square plate. The second case is that of a cylinder or ring. 

This statement will, perhaps, serve to convey some notion of our 
author's treatment of the several special systems of vibrating bodies. 
Of the contents of Chapters 4 and 5, which treat of vibrating sys- 
tems in general, it is not easy to write without going into details 
such as our limits will not allow. Partly this is due to the ex- 
treme generality of the statements : e, g, such a statement as this — 
A force of any type acting alone produces in a system a displace- 
ment of a second type from the zero configuration equal to a dis- 
placement of the first type due to the action of an equal force of 
the second type — is scarcely intelligible apart from the reasoning 
by which it is proved, though a particular case mentioned by way 
of illustration is plain enough : — *' If A and B be two points of a 
rod supported horizontally in any manner, the vertical deflection at 
A when a weight W is attached at B, is the same as the deflection 
at B when W is applied at A " (p. 69). So, again, '* Young's 
Theorem " (p. 144) is perfectly intelligible as a simple statement, 
but in its generalized fwm (p. 99) it is almost unintelligible without 
its context. 

One important point in these chapters may be mentioned, viz. 
the introduction into the Equations of Motion of a function (F) 
caUed the *' dissipation function," to represent the forces arising 
from friction and viscosity, F being a homogeneous quadratic 
function of the velocities. The author, it must be added, has done 
every thing that could well be expected to smooth down the asperi- 
ties of a very difficult subject, both in the way of illustration and 

F2 

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68 Royal Society: — 

example, and particularly in regard to the difficulties incident to 
the treatment of " Vibrating Systems in general." He has done 
this by his elaborate discussion of the case of a vibrating system 
having one degree of freedom, which, as already mentioned, forms 
the subject of Chapter 3, as well as by the discussion oE the system 
having two degrees of freedom at the end of Chapter 6. 

The complaint has often been made, and with regard to \A4dely 
different subjects, that, with a few conspicuous exceptions, our 
beet scholars and ablest men of science do not write— that they 
content themselves with the pleasant task of acquiring knowledge, 
and possibly of adding to it by means of brief memoirs which are 
apt to be lost in the waste sea of the literature of Memoirs and 
Periodicals. The last st/ep between acquiring the knowledge, and 
drawing up a formal statement of it for the benefit of others in- 
volves kbour which they decline to take*. The present volume is 
a striking exception to the common practice. Its noble author 
might well have considered himself absolved from the irksome labour 
of writing a book, a task which he might have regarded as falling 
more properly to the lot of the professional mathematician. We 
do not doubt that this consideration will add to the gratitude of 
students, who will find in the work before us a means by which their 
labours in this branch of science will be most materially lightened. 



XII. Proceedings of Learned Societies. 

ROYAL SOCIETY. 

[Continued from vol. iv. p. 895.] 

April 26, 1877.— Dr. J. Dalton Hooker, C.B., President, in the 

Chair. 

'PHE following paper was read : — 

-*- ** On Repulsion resulting from Badiation. — Preliminary Note 

on the Otheoscope.'' By William Crookes, F.R.S. Ac. 

I communicated to the Eoyal Society in November last an 
account of some radiometers which I had made with the object 
of putting to experimental proof the " molecular pressure " theory 
of the repulsion resulting from radiation. Continuing these re- 
searches, 1 have constructed other instruments, in which a movable 
fly is caused to rotate by the molecular pressure generated on 
fixed parts of the apparatus. 

In the radiometer, the surface which produces the molecular 
disturbance is mounted on a fly, and is driven backwards by the 
excess of pressure between it and the sides of the containing vessel. 
Begarding the radiometer as a heat-engine, it is seen to be im- 

* "Not the least of the many beneflts which he conferred waa the example 
he Bet of unceasing kbour ; for this was a permanent rebuke to that indolence 
which IS the besetting failing of the place — not the grosser form of aimless waste 
of time, but the more seduotiTe error which consists in the mere acquisition of 
knowledge, which is never reproduced for the benefit of others."~Todhunter'B 
Account of the Writings of W. Whewell, voL i pp. 415, 416. 



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Mr. W- Crookes on the Otheoscope. 69 

perfect in many respects. The black or driving surface, correspond- 
ing to the heater of the engine, being also pcurt of the moving fly, 
is restricted as to weight, material, and area of surface. It must 
be of the lightest possible construction, or friction will greatly 
interfere with its movement; it must not expose much surface, or 
it will be too heavy ; and it must be a very bad conductor of heat, 
so as to retain the excess of pressure on one side. Again, the part 
corresponding to the cooler of the engine (the side of the glass 
bulb) admits of but little modification. It must almost necessarily 
be of glass, by no means the best material for the purpose ; it is 
obliged to be of one particular shape ; and it cannot be brought yery 
near the driving surface. 

A perfect instrument would be one in which the heaUr was sta- 
tionary; it might then be of the most suitable material, of sufEdent 
area of surface, and of the most efficient shape, irrespective of weight. 
The cooler should be the part which moves ; it should be as close as 
possible to the heater, and of the best size, shape, and weight for 
utilizmg the force impinging on it. By having the driving surface 
of large size, and making it of a good conductor of heat, such as 
silver, gold, or copper, a very faint amount of incident radiation 
saffices to produce motion. The black surface acts as if a molecular* 
vind were blowing from it, principally in a direction normal to 
the feurface. This wind blows away whatever easily movable body 
happens to be in front of it, irrespective of colour, shape, or material ; 
and in its capability of deflection from one surface to another, its 
urest by solid bodies, and its tangential action, it behaves in most 
respects like an actual wind. 

whilst the radiometer admits of but few modifications, such an 
iDstrument as the one here sketched out, is capable of an almost 
endless yariety of forms ; and as it is essentially different in its 
eonstruction and mode of action to the radiometer, I propose to 
identify it by a distinctive name, and call it the Otheoscope (wOcm, 
I propel). 

The glass bulb is an essential portion of the machinery of the 
radiometer, without which the fly ^lould not move; but in the 
otheoscope the glass vessel simply acts as a preserver of the requsite 
'amount of rarefaction. Carry a radiometer to a point in space where 
the atmospheric pressure is equal to, say, one millimetre of mercury, 
and remove the glass bulb ; the fly will not move, however strong 
the incident radiation. But place the otheoscope in the same con- 
ditions, and it will move as well without the case as with it. 

In the preliminary note already referred tot, I described a piece of 
apparatus by which I was able to measure the thickness of the layer 
of molecular pressure generated when radiation impinged on a 

* Molecular, not molar. There is no wind in the sense of an actual trans- 
ference of air from one place to another. This molecular movement may be 
compared to the movement of the gases when water is decompose! by an electric 
eurrent. In the water connecting the two polee there is no apparent movement, 
although eight times as much matter is passing one way as tne other. 

t Proc. Royal Soc. Not. 16, 1876, p. 310. 



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70 Royal Society: — 

blackened surface at any degree of exhaustion. At the ordinary 
density of the atmosphere the existence of this molecular disturbance 
was detected several millimetres off, and its intensity increased 
largely as the generating surface and movable plate were brought 
closer together. It would be possible, therefore, to construct aa 
otheoscope in which no rarefaction or containing vessel was neces- 
sary, but in which motion would take place in air at the normal 
density*. Such a heat-engine would probably work very well in 
sunlight. 

Aided by the mechanical dexterity of my assistant, Mr. C. H. 
Gimingham, I have constructed several varieties of otheoscope. 
These will be exhibited at the Soiree of the Boyal Society on 
Wednesday next, as illustrations of the very beautiful manner in 
which, at this stage of my investigations, theory and experiment 
proceed hand in hand, alternately assisting each other, and enlarging 
our knowledge of those laws of molecular movement which con- 
stitute a key to the relations of force and matter. 

The following is a list of the otheoscopes I have already made, 
together with some new experimental radiometers, which will be 
exhibited for the first time on Wednesday : — 

1. Otheoscope. — A four-armed fly, carrying four vanes of thin clear 
mica, is mounted like a radiometer in an exhfusted glass bulb. 
At one side of the bulb a plate of mica blacked one side is fastened 
in a vertical plane, in such a position that each clear vane in rotating 
shall pass the plat-e, leaving a space between of about a millimetre. 
If a candle is brought near, and by means of a shade the light 
is allowed to fall only on the clear vanes, no motion is produced ; 
but if the light shines on the black plate, the fly instantly rotates 
as if a wind were issuing from this surface, and keeps on moving as 
long as the light is near. 

2. Otheoscope. — ^A four-armed fly carries roasted mica vanes, 
and is mounted in an exhausted glass bulb like a radiomet^er. 
Fixed to the side of the bulb are three plates of clear mica, equi- 
distant from each other in a vertical plane, but oblique to the axis. 
A candle brought near the fixed plates generates molecular pressure, 
which, falling obliquely on the fly, causes it to rotate. 

3. Otheoscope, — A large horizontal disk revolving by the mo- 
lecular disturbance on the surface of inclined metallic vanes, which 
are blacked on both sides in order to absorb the maximum amount 
of radiation. 

4. Otheoscope. — Inclined aluminium vanes driven by the mo- 
lecular disturbance from the fixed black mica disk below, blowing (so 
to speak) through them. 

5. Otheoscope. — ^A large horisontal coloured disk of roasted mica, 
driven by inclined aluminium vanes placed underneath it. 

6. Otheoscope, — A bright aluminium disk cut in segments, and 
each segment turned at an angle, driven by a similar one below of 
lampblacked silver. 

* Since writiiig this I have constructed such an instrument The movement 
takes place in the way I had anticipated.— W. C, April 26th, 1S77. 



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Mr. W. Crookes on tlie Otheoscope. 71 

7. Radiometer, — A rertical radiometer, made with eight disks of 
mica bhicked on one side, and the whole suspended on a horizontal 
axis which works in two glass cups. The motion of the radiometer 
is assisted on each side by driving vanes of aluminium blacked on 
(me side. 

8. Radiometer. — A vertical turbine radiometer, the oval vanes of 
roasted mica blacked on one side. 

9. Radiometer, — A, spiral radiometer of roasted mica blacked on 
the upper side. 

10. Radiometer of large size, showing great sensitiveness. 

11. Radiometer, — A two-disk radiometer, the flj carrying roasted 
mica disks blacked on one side ; in front of each black surface is 
fixed a large disk of thin clear mica. The molecular disturbance 
set np on the black surface, and streaming from it, is reflected in 
the opposite direction by the clear plate of mica, causing the fly 
to move abnormally, i. e, the black surface towards the light. 

12. Radiometer, — A two-disk radiometer, the fly carrying roasted 
mica disks blacked on one side, similar to No. 11, but with a large 
elear disk on each side. The molecular disturbance, prevented 
from being reflected backwards by the second clear disk, is thus 
eaused to expand itself in a vertic^ plane, the result being a total 
loss of sensitiveness. 

13. Radiometer, — A two-disk, cup-shaped, aluminium radiometer, 
hang opposite ways ; both sides bright. Exposed to a standard 
candle 3'5 inches off, the fly rotates continuously at the rate of 
one reTolution in 3*37 seconds. A screen placed in front, so as to 
let the light shine only on the convex surface, produces repulsion 
of the latter, causing continuous rotation at the rate of one revolu- 
tion in 7*5 seconds. When the convex side is screened off, so as 
to let the light shine only on the concave, continuous rotation is 
produced at the rate of one revolution in 6-95 seconds, the concave 
side being apparently attracted. These experiments show that the 
repulsive action of radiation on the convex side is about equal to 
the attractive action of radiation on the concave side, and that the 
double speed with which the fly moves when no screen is interposed 
is the sum of the attractive and repulsive actions. 

14. Radiometer, — ^A two-disk, cup-shaped, aluminium radiometer, 
lampblacked on the concave surfaces. In this instrument the usual 
action of light is reversed, rotation taking place, the bright convex 
side being repelled, and the black concave attracted. When the 
light shines only on the bright convex side, no movement is pro- 
duced ; but when it shines on the black concave side, this is at- 
tracted, producing rotation. 

15. Radiometer. — ^A cup- shaped radiometer similar to the above, 
but having the convex surfaces black and the concave bright. Light 
shining on this instrument causes it to rotate rapidly, the convex 
black being repelled. No movement is produced on letting the 
light shine on the bright concave surface, but good rotation is 
produced when only the black convex surface is illuminated. 

16. Radiometer. — A multiple-disk, cup-shaped, turbine radio- 



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72 Geological Society:— 

meter, bright on both rides, workin'g by the action of warm water 
below and the cooling effect of the air. above. 

17. Radiometer, — A. four-armed, metallic radi<«ieter with deep 
cups, bright on both rides. 

18. Radiometer. — A four-armed radiometer, the vanes consisting 
of mica cups, bright on both sidea. 

19. Radiometer, — A four-armed radiometer having dear mica 
vanes, the direction of motion being determined by the angle formed 
by the mica vanes with the inner surface of the glass bulb. 



GEOLOGICAL SOCIETY. 
[Continued from vol. iv. p. 312.] 

November 21, 1877.— John Evans, Esq., F.R.S., D.C.L., Viee- 
President, in the Chair. 

The foDowing communications were read r — 

1. •* On the Glacial deposits of West Cheshire, together with lists 
of the fauna found in the Drift of Cheshire and adjoining Counties.** 
By W. Shone, Esq., F.G.S. 

The conclusions arrived at by the author in this paper were as 
follows. Like Prof. Hull, he distinguished a triple division of the 
deposits under consideration. 1. The Lower Boulder-clay, or, as he 
preferred to call it. Lower Glacial Drift, resting immediately upon 
the eroded surface of the Keuper, consists for the most part of com- 
pact clay, containing numerous and large striated erratics, together 
with a fauna of Scandinavian type, the Gasteropoda being generally 
filled with fine silt containing Microzoa. The author believed that 
the shells found in this deposit were principally distributed by ground- 
ice, which took them up and floated them off the shore. 2. Tho 
Middle Sands and Gravels, or Interglacial Drift of the author, con- 
sist chiefly of sands and gravels containing few (if any) glaciated 
stones. The fauna of this division is Celtic, with a few Scandina- 
vian species derived from the Lower Boulder-clay ; the shells were 
distributed principally by currents ; and the Gasteropoda were seldom, 
if ever, filled with sand containing Microzoa. 3. The Upper Boulder- 
clay, or Upper Glacial Drift, is composed for the most part of clay 
not so compact as tho Lower Boulder-clay, and containing fewer and 
smaller glaciated stones, which are more abundant near the base. 
T^e^fauna is Scandinavian at the base of the beds. The shells were 
distributed principally by ground-ice, and those of southern typo 
derived from tho Middle Sands and Gravels. The Gasteropoda are 
chiefly filled with silt containing Microzoa. The paper was accom- 
panied by lists and tiibles of fossils, a large collection of which was 
exhibited in illustration of the paper. 

[The Chair was then taken by Warington Smyth, Esq., MA., 
F.K.S., F.G.S.] 

2. " The Moffat Series.'' By C. Lapworth, Esq., F.Gr.S. 

The fossils found in the highly convoluted Lower Silurian rocks 
of the southern uplands of Scotland are usually restricted to certain 



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Mr. C. Lapworth on the Moffat Series. 73 

oaiTOW bands of black carbonaceotis and Graptolitic shales, which, 
from their especial abundance in the neighbonrhood of the town of 
Moffat, Dumfriesshire, are known to geologists as the Moffat Shales 
or Moffat Series. 

The most perfect section of the black shales visible within the 
Moffat area is exhibited in the cliffs of the gorge of Dobb's linn, at 
the head of Moffatdale. It was shown by the author that they are here 
disposed in a broken and partially inverted anticlinal, which throws 
off on both sides the basal beds of the surrounding non-fossiliferous 
grey wackes. They are distinctly arranged in three successive groups 
or divisions. Each of these divisions is distinguished by special 
lithological characteristics, and possesses a distinct fauna. To the 
lower and middle divisions a few fossils are common ; but between 
the middle and upper divisioDs the palseontological break is com- 
plete. These divisions, again, are naturally subdivided into several 
zones, each characterized by special species or groups of species. 

A larger exposure of the same deposits occurs at Craigmichan, a 
few miles to the south-west, where the beds of the lower division 
are shown to a much greater depth than at Dobb*s Linn. In these 
two localities the general succession of the GraptoHtic shales is as 
follows : — 

feet. 

^'^ St f (*) ^PP*' ^'*"" {*"g:ro'f E'ln'd"^&r 70 to 80 

Moffat, 
(a) Glenkiln\ 
Shales,or I 
Lower f 
Moffat. J 



I (a) Lower Hartfell Black hard daty shales and flags 40 to 50 



Yellow and grey shales and flags, 
non-fossil iferous, with a few 
hands of soft hlack Graptolitic 
shales 150 



^ith the aid afforded by these sections, the thorough investigation 
of the ten subparaUel black shale-bands of the Moffat area is ren- 
dered a matter of ease and certainty. Of these, the four bands 
lying to the south-west of Saint Mary's Loch are the most con- 
tinuous. They were described in detail by the author ; and it was 
shown that in each the only strata apparent are indisputably those 
of the type sections of Dobb's Linn and Craigmichan, with j^hich 
they agree zone for zone in sequence and in all their characters, 
mineralogical and zoological. Here, also, the beds are arranged in 
greatly elongated anticlinal foims, the axes of which are, as a rule, 
inverted. In any single transverse section, the succession of the 
beds on the opposite sides of the median line of the band is identical ; 
and the highest zone of the black shtJes everywhere passes up con- 
formably into the basal bed of the surrounding greywackes. The 
varying width of the band is dependent simply upon the varying 
elevation of the crown of the anticlinal. "Where the band is of least 
diameter, only the highest beds of the Birkhill shales rise from 
below the greywackes. As the band expands, tho underlying zones 



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74 Geological Society. 

emerge one by one in its centre, till finally, in the widest exposures, 
we recognize the deepest strata of the Glenkiln shales. 

It was shown, by plans, sections, and descriptions of every expo- 
sure of consequence within the Moffat district, that precisely similar 
results are arrived at with respect to the remaining black shale- 
bands. To the south of Moffatdale, the Moffat beds agree essentially 
with those of Dobb's linn ; but to the north the whole formation 
diminishes in collective thickness, and the highest division gradually 
loses its fossiliferous black shales. 

These facts place it beyond question that all the carbonaceous and 
Graptolitiferous shales of the Moffat area are portions of one and the 
same originally continuous deposit — ^the Moffat Series^ which is now 
the oldest visible rock-group in the district, being everywhere in- 
ferior to the prevailing gre^^wackes, through which it invariably 
rises from below in greatly elongated anticlinal forms. 

In the rigid restriction of distinct groups of fossils to a few feet 
of the succession, the rocks of the Moffat series resemble the thin- 
bedded Silurians of Scandinavia and North-eastern America. From 
analogy it may be suspected that they similarly represent an enor- 
mous period of time. The correctness of this inference is demon- 
strated by the evidence afforded by the known geological range of 
their organic remains. The Graptolithina of the Lower or Glenkiln 
division are those of the highest Llandeilo Flags of Wales, the 
corresponding Middle Dicranograptus-schista of Sweden, and the 
Norman's-Kiln shales that underlie the Trenton (Bala) limestone of 
New York. The Hartfell species occur in the Bala beds of Conway, 
&c., the higher JHcranograptus-schiats of Sweden, and the Utica 
and Lorraine shales that overlie the Trenton limestone. Those of 
the Birkhill shales agree almost species for species with the fossils 
of the Coniston Mudstone of Cumberland, the Kiesel-Schiefer of 
Thuringia, and the Lobiferous beds of Sweden, which lie at the 
summit of the Lower Silurians of their respective countries. Hence 
it may be considered certain that the Glenkiln shales are of highest 
Llandeilo age, that the Hartfell shales stand in the place of the Bala 
or Caradoc of Siluria, and that the Birkhill shales correspond to the 
Lower Llandovery. 

The insignificant thickness of these three formations in the Moffat 
distiict is in strict agreement with the well-known north-westerly 
attenuation of the Lower Silurian rocks in Wales, England, and in 
Western Europe generally. 

It was pointed out that these results, when carried to their 
legitimate conclusion, harmonize all the apparently conflicting facts 
hitherto collected among the Lower Silurians of the south of Scot- 
land. We have a complete explanation of such difficulties as the 
remarkable lithological uniformity of the predominating strata, the 
absence of associated igneous rocks, the peculiar localization of 
the fossils, their identity along certain lines, and their rapid and 
peculiar impoverishment along others. We reduce, at a single 
stroke, the apparently gigantic thickness of the South Scottish 
Silurians to reasonable limits, and at the same time bring them into 
perfect harmony with those of Western Europe and America. 

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[ 75 ] 
XIII. Intelligence and Miscellaneoits Articles. 

OS THK COMPOSITION AND THE INDUSTRIAL USE OF THE GASES 

ISSUING FROM METALLURGIC HEARTHS. BY L. CAILLETET. 
T^HE remarkable investigations of H. Sainte-Claire Deville on dis- 
-■• sociation, in opening to science a new path of research, have 
likewise promised to interpret a great number of metaUurgical 
phenomena which had till then remained unexplained. 

By coUecting the gases which circulate in the hottest part of the 
fornaces in which iron is worked, I have been able, by means of 
apparatus similar to M. Deville* s, to prove that the composition of 
those gases, suddenly cooled, is totally different from the results 
given by the analyses of Ebelmen. Tliat skilful metallurgist, unac- 
quainted with the phenomena of dissociation, collected the gases by 
slowly aspirating them by means of a long tube — which necessarily 
brought about the combination of their dissociated elements. 

In Ebelmen's analyses the reaction seems almost always com- 
plete, while the cooling undergone by the gases shows that smoke 
and csrburetted gases can subsist in presence of oxygen at the tem- 
perature of welding iron. 

The gases collected at the top of the grating of an annealing-oven, 
at a point where the temperature is such that the eye cannot sup- 
port the brighfcness of the bricks raised to a most intense whiteness, 
contain : — 

Oxygen 13-15 

Carbonic oxide 3*31 

Carbonic acid 1-04 

•Nitrogen (by difference) . . 82-50 

100-00 
Independently of the carbonic oxide, there is found in the oxi- 
dising atmosphere of the oven a large excess of finely divided carbon, 
which deposits itself on the tube, hot and cold, which serves for the 
aspiration. 

In metallurgic works the gases issuing from welding-fires are 
generally conducted beneath generators, which thus produce with- 
out expense the supply necessary for the working of engines. The 
gases, therefore, rapidly cool against the walls of the boiler ; thus, 
after traversing a length of 15 metres, their temperature is below 
500''. They are then formed of 

Oxygen 7-65 

Carbonic oxide 3-21 

Carbonic acid 7*42 

Nitrogen (by difference). . 81-72 

100-00 

It may be concluded from this analysis that the quantity of 

oxygen has diminished by nearly one half, in reacting, not upon 

the carbonic oxide, of which the proportion has changed but little, 

but upon the finely divided carbon, which exists in large quantity. 



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76 Intelligence and Miscellaneous Articles. 

as I have shown, in the atmosphere of the hearth. The cooh'ng and 
extinction of the gases stops all reaction ; and when the latter are 
thrown off by the chimney they still Contain, as we see, large quan- 
tities of combustible materials. 

The investigations which I have made for the purpose of taking 
up a portion of these gases, left hitherto unused, have demonstrated 
that it is easy to rekindle them by passing them over a fire, at the 
same time retarding their motion. It was with this view that, in 
my forges at Saint- Marc (Cote d'Or), I had a furnace of large di- 
mensions set up to receive the gases as they issued from the gene- 
rator. On arriving in this furnace, the section of which is more 
than 3 square metres, the gases lose a large portion of their velo • 
city, at the same time that they are kindled in passing over a small 
grating on which coal-cinders, or some combustible of small value, 
are burned. 

The high temperature developed in these conditions is utilized in 
my works for the annealing of sheet-iron. It is, in fact, known that 
roiling renders the iron brittle, and that it becomes covered with 
adherent oxide in the annealing- ovens. By heating the sheets thus 
altered for twelve hours in cast-iron boxes well closed, arranged in 
the gas -oven just mentioned, the sheets are found, after complete 
cooling, to have become perfectly malleable ; and the oxide has dis- 
appeared, leaving the surfaces clean and bright. This reduction is 
easily •explained if we remember the beautiful researches of MM. H. 
Sainte-Claire Deville and Troost on the passage of hydrogen through 
red-hot metals. I have likewise had the honour to communicate 
to the Academy* various experiments which prove that, on plun- 
ging a flattened iron tube into a fire, hydrogen passes through its 
sides, and, accumulating within it, causes it to resume its original 
form. The gases which have penetrated into the cast-iron box 
under the influence of the red-hot sides are therefore essentially 
reducing, and produce in a very short time complete deoxidation of 
the metallic surfaces. 

In brief, we may conclude from my experiments : — 

1. That the gases issuing from metallurgic fires still contain, 
even after passing under steam-generators, an important quantity 
of combustible principles, and that, with the aid of the processes 
above described, it is easy to kindle them afresh and bum them 
almost completely. 

2. That the passage of reducing gases through the red-hot me- 
tallic walls is capable of receiving applications in metallurgy which 
doubtless will not be limited to the particular case of which I have 
given an account. — Comptes Mendus de VAcadimie des Sciences^ 
Nov. 19, 1877, tome Ixxxv. pp. 955-957. 



ON A PILE IN WHICH THE ATTACKABLE ELECTRODE IS OF COKE. 
BY P. JABLOCHKOFF. 

The coke burned in steam-engines produces work which, trans- 
• Coniptes lUndus, t. Iviii. pp. 327, 1067. 



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Intelligence arid ARscellaneous Articles. 77 

formed into electricity by means of magneto-electric machines, 
supplies this electiicitj much more economically than any chemical- 
action pile that has hitherto existed. This consideration gave me 
the idea of producing electricity by attacking coke directly. But, 
as every one knows, coke is not attacked by any liquid at ordinary 
temperatures; I was therefore obliged to construct an electro- 
chemical pile with hot liquid. 

Now it was evident that bodies which are liquid at ordinary 
temperatures would be vaporized at the temperature necessary for 
attacking coke. Hence it was necessary to take a substance which 
would only become liquid at a sufficiently elevated temperature, 
and be converted into vapour only at a very high temperature. 

With this view 1 fused either nitrate of potass or nitrate of soda; 
and in this liquid I immersed as attackable electrode ordinary coke, 
and platinum as the uuattackable electrode. But experience has 
proved to me that this latter electrode may be iron, cast iron, or 
any other metal which in the presence of coke is not attacked by 
the liquid. 

By adding different metallic salts one can vary the electromo- 
tive force of the pile, the velocity of combustion of the coke ; and 
with those salts the galvanoplastic deposit of the metals is received 
npoa the unattackable electrode. 

The electromotive force of the pile varies between 2 and 3 units, 
according to the nature of the metallic salts introduced ia^ the 
liquid ; this force is therefore superior to that of either the Buusen 
or the Grenet pile ; indeed the Bunsen pile gives the maximum of 
1*8 unit, the Qrenet pile 2 or, in the most favourable conditions, 
2*1 units. 

To set the pile in action in the most practical manner, it is not 
necessary to fuse the alkaline nitrate beforehand; it suffices to ignite 
a piece of coke and put it in contact with the nitrate in powder. 
Chemical action commences immediately ; the temperature produced 
fuses the salt which surrounds the coke ; and the pile enters upon 
its functions. During the activity of the pile much carbonic acid 
aod other gases are liberated. I have devised an arrangement per- 
mitting the gas to be stored, in order to make it serve as a motive 
power. The foUowing is the practical arrangement of the elements 
of the pile : — 

^ A cast-iron pot, of a cylindrical shape, serves at the same time 
as receiver and unattackable electrode. An iron-wire basket, of 
concentric form, serves for holding the coke, and at the same time 
plays the part of a rheophore. As the coke and fused salt are con- 
sumed, fresh quantities of both substances can be added by hand, 
or the pile can be fed automatically, during the whole time of the 
operation. Contrary to what might have been thought, the com- 
bustion is not at all rapid. 

Therefore, by this process, direct combustion of coke gives the 
electric current, the deposition of metals, and a motive power. — 
Compies Rendus de VActicUmie des Sciences^ Dec. 3, 1877, tome 
IxxxY. pp. 1062, 1063. 



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78 Intelligence and Miscellaneous Articles^ 

ON THE LAW OF ABSORPTION OF RADIATIONS THROUGH BODIES, 
AND ITS EMPLOYMENT IN QUANTITATIVE SPECTRAL ANALYSIS 
(part I.). BY G. GOVI. 

When we interpose an absorbent medium in the path of the 
white light which passes through the slit of a spectroscope, we 
usually see dark bands appear in difEerent parts of the spectrum, 
which there diminish the brightness of the colours or even com- 
pletely extinguishes them. It is seldom that these bands do not 
invade a great number of contiguous wave-lengths, which they ob- 
scure in spreading more feebly on both sides of a more intense line 
of absorption. If the thickness of the absorbent medium be aug- 
mented, fresh shaded bands often appear between the former ones ; 
but what never fails to be produced is the strengthening of the 
first bands and their progressive dilatation ; so that, for a certain 
thickness of the medium, the entire spectrum is invaded by the 
shade, and so much enfeebled that it may be regarded as quite ex- 
tinguished. 

This progressive widening of the absorption-bands singularly 
reminds one of the increase in number and the dilatation of the 
bright lines which several observers have verified in the spectra of 
incandescent gases in proportion as their rarefaction is diminished 
and their temperature augmented ; so that it is quite possible the 
two uhenomena may correspond and be complementary the one to 
the other for one and the same substance. Moreover all the radia- 
tions, visible and invisible, of the spectrum present analogous phe- 
nomena ; and if we here speak of the luminous radiations only, it is 
solely because their study is much more convenient and more usual 
than that of the ultra-red or ultra-violet radiations. 

It is obvious, from what has just been said, that the absorptive 
power of a substance is not sumciently characterized by sudi or 
such a dark band appearing in the spectrum of the white light 
which has passed through a certain liuckness of it, and that, in 
order to define it perfectly, we must know all the modifications it 
can determine in the spectrum, from the sb'ghtest and most limited 
up to that which produces sensible extinction of all the radiations. 
In other words, we do not truly know the absorptive power of a 
substance unless we have determined its coefiicients of absorption 
for all the wave-lengths that can be studied, from those correspond- 
ing to obscure heat to those met with at the limit of photogenic 
action. 

This is why Sir J. Herschel, and many others after him, have 
attempted to construct, through points, the curves which were to 
express the values of the absorption-coefficients, as functions of 
the wave-lengths, for different bodies ; but the discontinuity of the 
artifices employed, and the absence of every photometric measure, 
have hitherto permitted only very incomplete results to be obtained. 
It is nevertheless not impossible to obtain a more rigorous defini- 
tion of the absorptive power of bodies, either by making directly 
apparent to sight the curves themselves of equal chromatic absorp- 



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Intelligence and MueeUaneouB Articles, 79 

tion in their entire deyelopment, or by measuring the luminous in- 
tensity aloDg the whole extent of the spectrum in order afterwards 
to deduce therefrom the corresponding coefHcients of absorption. 
It suffices for observing directly the spectral curves of equal ab- 
sorption *, to give to the absorbent the form of a prism (or, more 
strictly speaking, of a wedge) more or less acute, which is applied 
by one of its plane faces close to the slit of a spectroscope. The 
edge of this prism is placed at one end of the slit, parallel to its 
width ; and we find that we thus have, over the entire length of 
the opening, an absorbent medium, the thickness of which increases 
uniformly from zero (at the edge) up to a certain maximum de- 
pending on the angle of the prism and the length of the slit. 

The deviation due to the prismatic form of the medium is to be 
destroyed by opposing to the first a second prism of a material as 
little absorptive as possible (rock-salt, fluor-spar, quartz, glass, 
water, alcohol, &c.). The angle of this second prism is easily cal- 
culated approximately, which is sufficient in most cases ; but it can 
at need be rendered variable within limits sufficiently wide for 
giving at all times almost perfect compensation. 

When in this way an absorbent medium of variable thickness is 
placed in front of the slit of a spectroscope illuminated with per- 
fectly white Ught (that of incandescent solids), the spectrum no 
longer appears, as usually, uniformly luminous throughout its 
height, but in it shades are distinguished more or less undulated or 
toothed, which exhibit immediately to the eye the law according to 
which the absorption-coefficient of the medium varies with the 
wave-length of the incident light. 

These curvee can be constructed by drawing them with the 
camera lucida, by fixing them by photography, or by referring them 
to two rectangular axes by aid of two luminous micrometers seen 
by reflection — one fixed parallel to the length of the spectrum, the 
other movable and normal to the first. All these means, however, 
of constructing the curves of chromatic absorption suppose that it 
is possible to recognize in them the points of equal intensity, which 
is not very easy ; but it is useful to have recourse to them to re- 
present the complete form of the law of absorption when we have 
to do with sufficiently absorbent substances and when rigorously 
exact measurements are not indispensable. 

If the slit be divided into two parts in the direction of its length, 
and each of the two halves be employed for producing a spectrum 
with curves of chromatic absorption, the two spectra being juxta- 
posed in the direction of their length, nothing will be easier than 
to compare their curves and to ascertoin the equality or the differ^ 
ences between them. We might even, by a tolerably simple arti- 
fice, slide one of two spectra, of one and the same absorbent mate- 
rial at two different degrees of concentration, over the other, 
ascertain the zones of equal intensity, and thus apply the spectro- 
scope to the proportioning of such substance. 

* ^ Metodo per determinare le ciirve 8]^ettrali d^assorbimento della luce 
nei varii mezzi," di Gilberto Govi {Noiizia storica dei lavori, ecc., delTAc^ 
cademia di Torino negli anni 1804 e 1865, adunanza dell' 8 maggio 1864). 

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80 Intelligence and Mwcellaneous Articles. 

The employment of solar light permits the reference of the ab- 
sorption-curves to the Fraunhofer lines, and consequently to the 
wave-lengths of the different points in the spectrum. If the 
prisms were replaced by networks, we should have a simpler repre- 
sentation of the relation connecting the coefficients of absorption 
with the different wave-lengths. When, however, we wish to 
study, with respect to chromatic absorption, substances endowed 
with a very feeble absorptive power, or desire to express more pre- 
cisely the law of extinction for all the radiations, the process just 
described is scarcely suitable. In this case photometric means 
must be used, and recourse be had to the law of monochromatic 
absorption admitted by physicists for interpreting the results. — 
Gmnptes Rendus de VAcademie des Sciences, Dec. 3, 1877, tome Ixxxv. 
pp. 1046-1049. ^ 

THE LIQUEFACTION OF OXYGEN. 
One of the most interesting experiments in physics of our times 
has just been performed at G-eneva, with rare success, in the works 
of the Physical-Instrument Manufacturing Company. Our fellow 
citizen, M. Kaoul Pictet, has succeeded in obtaining, by means of 
ingeniously combined apparatus, the liquefaction of oxygen gas. 
The following are, briefly, the principles by aid of which this impor- 
tant result has been obtained : — By a double circulation of sulphurous 
and carbonic adds the latter gas is liquefied at a temperature of 
65 degrees of cold under a pressure of 4-6 atmospheres. The 
liquefied carbonic acid is led into a tube of 4 metres length ; two 
combined-action pumps produce a barometric vacuum over this 
acid, which solidifies in consequence of the difference of pressure. 
Into this first tube (containing, as just said, solidified carbonic 
acid) passes a narrower tube, in which circulates a current of oxy- 
gen, produced in a generator containing chlorate of potass, and 
having the form of a large howitzer-shell with walls thick enough 
to prevent all risk of explosion. The pressure may be carried as 
far as 800 atmospheres. ' Yesterday morning, all the apparatus 
being arranged as just indicated, under a pressure not exceeding 
300 atmospheres, a liquid jet of oxygen spirted from the end of 
the tubes at the moment when the compressed and refrigerated gas 
was passing from this high pressure to the atmospheric. What 
gives to this fact its great scientific interest is, that it experimen- 
tally demonstrates the truth of the mechanical theory of heat, by 
proving that all gases are vapours, capable of passing through the 
three states — solid, liquid, and gaseous. A fortnight since, M. 
Cailletet had succeeded in liquefying nitric oxide, under a pressure 
of 146 atmospheres, and at 11 degrees of cold. After the experi- 
ment of M. Kaoul Pictet there remain only two gases that have as 
yet escaped the test of liquefaction — hydrogen and nitrogen. The 
fine experiment above described will, we are informed, be repeated 
on Monday next, and following days, \idth some slight changes in 
the processes and arrangement of apparatus. — Journal de OerUve^ 
December 23, 1877. 

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Phil.Ma4.S.o.Vol.5.Pl.lII. 



Fig.l. 








P N. 




/ 


rig.e. 




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c 




\ 
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Miniflm Bros . Uth. 



THE 
LONDON, EDINBURGH, and DUBLIN 

PHILOSOPHICAL MAGAZINE 

AND 

JOURNAL OF SCIEJTCE. 

[FIFTH SERIES.] 



FEBRUARY 1878. 



XIV. An Account of same Eaperiments on Rigidiiy produced by 

Centrifugal Force. * By John Aitken, F.R.S.E.\ 

[Plates UL-VII.] 

THE experiments do not contain much that is new, many 
of the problems having previously been mathematically 
wrooght out by Sir William Thomson and others. They, 
howerver, help to fill up a very evident gap in our experimental 
dynamics ; and it is hoped they will enable the general reader 
to form a clearer idea of the action of the so-called centrifugal 
force, a force the fundamental action of which is often mis- 
imderstood. This tendency to misunderstanding has arisen 
principally from two causes : — ^the one being the paucity of 
oor experimental illustrations of centriiiigai force (almost 
all our experiments only illustrate the action of this force 
roiind one centre and in one plane); the other cause being 
tbe name which has been applied to this force, the word centri- 
fugal meaning ^' to fly from the centre,'^ which has given rise 
to the idea that there is a force acting on a body when revolving 
round a centre tending to cause it to fly away from that 
oeDtre. If some word more correctly expressive of the action of 
this force could be introduced, it would do much to remove 
tbe present confusion. Professor James Thomson, in a paper 
before the British Association at Glasgow in 1876, objects to 
the word centrifugal, and only retains it on account of its veiy 

* fThe experiments were in part communicated to the Royal Society, 
Edinoiiighy and also in part to the Philosophical Societv of Glasgow, 
during the seesion 1875-7oy and slight accounts published in tneProceecungs 
of ihSfe Societies. A complete account, with drawings of the appaiatua, 
m now published for the first time.— W. T.] 

t Communicate^ bj Sir W. Thomson, Dec. 1877. 
Pka. Mag. S. 5. Vol. 5. No. 29. Feb. 1878. G 

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82 Mr, J. Aitken an some Kxperiments on 

general use. He has, however, some time ago suggested, and 
now generally uses, the word centreward in plaoe of centri- 
petal. It is much to be hoped that in his reforms he will not 
spare the word centrifugal, but will replace it by some word 
n^ore etymologically correct While objecting to the name 
centrifugal force, we are under the necessity of retaining it 
till some better term has been introduced. It will, however, 
be necessary for us clearly to understand what we mean by 
centrifugal force. According to the First Law of Motion, any 
body when in motion tends to move at a uniform velocity 
and in a straight line. If we wish the body to move in a 
circular or any curved path, then we must cause some force to 
act on it to compel it to deviate from its free path ; and the re- 
aistance which the body offers to this deviation is what we call 
centrifugal force. Or, more simply, centrifugal force is the re- 
sistance which a body ofiFers when in motion to change of 
direction of motion. If we remove the deviating force, then 
there is no centrifugal force, and the body simply tends to 
continue moving in a straight line*. 

Suppose now that, instead of one body revolving round a 
centre, we have a numl^r of bodies of the same mass, all 
moving at the same velocity, all placed at equal distances from 
each other and at equal distances from the centre, then we 
may cause this series of bodies to revolve round the centre by 
tying them to the centre, when they will exert a radial tension ; 
or we may cause them to revolve round the centre by linking 
all the bodies together like a chain. When such a series of 
bodies are in motion round a centre, they exert a pressure at 
right angles to the direction of their motion, the result of 
which is, a tension is produced in the system tending to burst 
the links, in the same manner as the tension is produced in the 
shell of a cylindrical boiler by the pressure of the steam. 
According to the dynamical theory of gaseous pressure, these 
two tensions are produced in a very similar manner — ^in the 
first by the resistance to change of direction of motion of the 
links, and in the second by the resistance to change of direc- 
tion of motion of the molecules of the steam. 

The tension produced in a series of bodies revolving round 
a centre is very simply illustrated by taking an elastic band 
and fitting it tightly over a pulley which can be driven at a 
great velocity, such as that shown in PI. IV. fie. 1, when it 
will be seen that as the velocity increases the tigntness of the 

* For rimplicity the body is here spoken of as a whole : and this is cor- 
rect if the body is infinitely small : but if the body is of any size and moves 
round a centre either outside the body or inside it, then we must consider 
each particle of the. body separately, as the di^rent parts of the body are 
moving at dififerent velocities and in different directions. 

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Rigidity produced by Centrifugal Force. 83 

elastic band on the ptillej diminifihes^ and if the velocity is 
soffi<dent it ceases to press on the pnlley ; and at length the ten- 
son produced by the centriftigal force opens ont the band to 
•odi a size that it becomes larger than the pnlley, its form and 
ifioti<Mi becoming irregular, and at last it flies off the pulley. 

If all the bodies in the system are moving at the same ve- 
locity and in paths of the same curvature (that is, in a circle), 
tben the tension and the centrifugal force will evidently be in 
equilibrinm at all points, and the chain will keep its circular 
shape, because, as the rate of deviation is the same for all 
Ae bodies, the resistance of each of the bodies to this devia- 
tion (or what we call the centrifugal force) will be the same at 
aD points, and the tension due to this resistance will also be 
ite same. The question may now be asked, Is this chain in a 
condition of stable or of uns^ble equilibrium ? If the circular 
form were to be slightly destroyed, would the chain tend to re- 
turn to the circular shape, or would it tend to depart further 
and farther from it ? J s the equilibrium of the chain the 
stable equilibrium of an egg resting on its side, or the unstable 
«qidfibrium of an egg balanced on its end ? The answer we 
thaQ get to this question will be that the equilibrium of the 
moving chain corresponds to neither of these forms, but might 
be compared to the equilibrium of a perfectly spherical and 
liomogeneons body resting on a perfectly horizontal plane, or 
floating in a fluid of the same specific gravity as itself, all 
positions being positions of equilibrium. 

First, let ns see what answer experiment gives to this ques- 
tion. If we hang an endless chain over a pulley, and the 
pulley is caused to rotate at a great velocity, it has long been 
well known that the motion so communicated to the chain 
bas but little tendency to alter the form of the curve in which 
the chain hangs, and that the principal effect of the motion is 
to OHifer on the chain a quasi-rigidity which enables it to re- 
Bst any force tending to alter its curvature. This statement 
must not, however, be taken as representing the facts of the 
ease rery accurately ; for while it may possibly be true of some 
ideal form of chain, yet I shall presently show that in all 
dttins we can experiment on there are forces in action in the 
moving chain which cause it to depart from the form it had 
vbile at rest; and if these forces were not balanced by 
ffRavitation, the form of the chain would soon become very 
diflSerent from what it was. 

What some of these disturbing forces are I shall point out 
bier on. For the present we shall neglect them, as in most 
chains tfaev are small, and shall simply consider the balance 
b^ween the oentrifueal force and the tension. When the 

G2 

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84 Mr. J. Aitken an some ExpeAments on 

chain moves in a circular path, the centrifugal force and the 
tension are evidently equal and balanced at all points ; and W0 
also know from experiment that, when the chain han^ in the 
form of a long loop from a pulley, the tension just balances 
the centrifugal force at all points, as the chain has no tendency 
when in motion to alter the form of the loop. I shall not 
attempt to enter into a mathematical investigation of this 
balance between these forces ; my province is simply to describe 
some experimental illustrations ; I would, however, refer all 
those who wish for a mathematical investigation of the subject 
to Thomson and Tait's * Elements of Natursu Philosophy,' where 
they will find it fully treated. There is, however, an extremely 
simple geometrical demonstration, which I may venture to give 
before proceeding further. 

Let us consider the equilibrium of an endless chain moving 
in a loop of such a form as that represented in fig. 7, PI. VII., 
the links of which are moving in a path of varying curvature. 
As the velocity of the links is the same at all points, it will 
not be necessary for us to consider how difierent velocities of 
the links will affect the tension in the chain ; and the investi- 

fation confines itself to the consideration of the tension pro- 
uced in the chain by the links when moving in paths of 
different rates and amounts of curvature. 

The first point to be considered is. What is the efiect of the 
rate oi curvature of the chain when the angle of deflection is the 
same ? Suppose A B C and D E F, fig. 1, PL III., to be two 
chains moving with the same velocity and in directions parallel 
to each other, and suppose the radius of the curved part of the 
path in D E F to be only one half of what it is in A B C. Now, 
as the deflection is the same in both cases, the integral forces 
required to produce these deflections will evidently be equal; 
or (to state it in another way) the force required to destroy 
the momentum in the chain in the direction A B, and to gene- 
rate momentum in a direction at right angles to A B, is the 
same in both cases. The whole resistance offered by all the 
links in the bend to this deflection, or what is called the 
centrifugal force, is therefore equal in both cases, and the ten* 
sions produced in the two chains will therefore be equal. So 
long, then, as the defiection is t/ie same the different rates of 
curvature produce the same tension in the chain, and have no 
tendency to alter the path in which the chain moves. The only 
difference between the two cases is, that the centrifugal force 
in the curved part of the chain D E F is twice as great per 
unit of length as in the curved part of A B C. Suppose, for 
instance, that there are 10 links in the bend in D E F, and 
&at each link exerts a force of 20 units. Then, as the radiua 



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Phil.Ma^. S 5.Vol.5.Pl VII. 
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Fig. 2 







Mintan^n n-*..^. 1;*V 



Rigidity produced by Centrifugal Force. 85 

in the bend in A B G is twice as great a& in D E F, there will 
be twice the number of links in A B C that there are in D E F, 
but the centrifugal force will only be one half what it is in 
D E F; so that in the bend in A B C we shall have 20 links each 
acting with a force of 10 units ; the result of which is^ the total 
force is the same in both cases^ namely200. 

The next point to be considered is, What is the effect of the 
cimount of bend or deflection on the tension of the chain ? 
Suppose the chain to be bent to the angle A B, fig. 2, PI. III., 
what tension will it put on the chain ? 

Let C D s= force required to destroy the whole momentum 
of the chain in the'line A D. 

Draw B E perpendicular to A D. Join D B. 
Then E D = force required to destroy momentum at the bend 

in the line A D ; 
and E B = force required to establish momentum in the 
direction P Q ; 
D B =s total deviating_ force at C required to produce 

the bend ACB; 
B D s the centrifugal force at C in direction and 
magnitude. 

On A C, C B construct the parallelogram A C B F. Join C F. 

F C is equal and parallel to B D ; 
/. F C = the centriragal force at the bend ACB. 

It is evident from the construction that F C is always equal 
to B D (that is, always equal to the centrifugal force), what- 
ever the angle ACB may be. 

The centrifugal force F G acting at the angle ACB will 
produce a tension in the chain equal to G A or G B, because 
F G is equal and opposite to the resultant of G A and G B ; and, 
further, it is evident from the construction, that, while the angle 
or bend A G B may vary and the centrifugal force F G vary 
along with it, the tension G A or G B does not vary. 

From these considerations we see that, though the centri- 
fugal force in a chain moving in such a path as that shown at 
fig. 7, PI. YIL, varies at the different points, being greater the 
quicker and the greater the curvature, yet the tension produced 
by the centrifugal force at the different points is the same, 
and is independent of the rate or the amount of curvature, and 
that therefore the chain while in motion has no tendency to 
alter its shape. 

These observations only refer to the tension in the chain 
produced by centrifugal force. It is, however, necessary for 
us, in order to understand some of the residts we shall presently 
see, to remember that there are other tensions in the chain 
besides this one. Tliere 18, for instance, the tension produced by 



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86 Mr, J. Aitken on some EaperimetUs an 

gravitation; this tension varies at different points, being nothing 
at the lowest point and increasing to a maximum at the highest 
point of the chain : and there is also the tension produced by 
patting and keeping the chain in motion; this tension is greatest 
at the part of the chain approaching the driving puUej^ and 
least at the part just leaving it. 

Description of Apparatus. 

Before proceeding to the experiments, it will be necessary 
for me briefly to describe the apparatus used. As chains were 
used in almost all the experiments, the object of the apparatus 
was simply to communicate in different ways motion to these 
chains ; the apparatus was therefore of the simplest description 
possible, and is represented to scale in figs. 1 to 5, PI. lY. 
Fig. 1 is a general view of the principal part of the apparatus. 
A short steel spindle, a, running in a tube, is mounted hori- 
zontally on the triangular supports 6 6 at a convenient height 
for making the experiments ; on one end of the shaft, a, is an 
arrangement, e, for fixing on the different sizes and shapes of 
pulleys shown in fig. 2. On the other end of the shaft is the 
small brass pulley d^ 1^ inch in diameter ; e is the driving-wheel 
made of wood, 2 feet in diameter, having a groove for a driving- 
cord cut in its circumference. The driving-wheel, «, is fitted to 
the end of a horizontal axle running in the bearings, //; the 
bearings are cast in one piece with the plate g^ which is held 
firmly to the sole-plate A by means of the two screws 1 1, which 
pass through longitudinal openings in the plate g to admit of 
the wheel being moved in a longitudinal direction for the 
purpose of adjusting it to the proper distance from the pulley 
d to keep the driving-cord k tight*. The driving-wheel is 
driven by means of the handle I ; and motion is communicated 
to the small spindle a by means of the cord k. The driving- 
wheel is easihr unmounted from its axle ; and the triangular 
supports ara nxed to the sole-plate by means of two long bolts 
passing through both supports and clamping them firmly to the 
sole-plate. l£e tube carrying the spindle a being also held 
by screws to the supports b b, the whole apparatus is easily 
unmounted for packing away. 

The chain, n, to be experimented on is hung over the pulley 
A fitted to c on the end of the spindle a, and the pulley put 
into rapid motion by means of the handle Z. As the small 
shaft makes about 13 revolutions for one of the driving-wheel, 

* If a small india-rubber band, such as those sold by stationers, is stretched 
over the grove in the pulley d, the friction between the cord and the pulley 
is very greatly increased, and the tightness of the cord becomes a matter of 
less importance. 



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Bigidihf produced by CerUnfu^ Force. 87 

a velocity of from 40 to 70 feet per Beoond may easily be com- 
municated to the chains. 

The pulleys for fitting to the spindle a are of different forms 
and sizes, and are shown to scale at A, B, C, D, fig. 2 ; their 
uses will be pointed out in describing the experiments. 

Very light chains were used, as many experiments can be 
made with light chains which would bo dangerous or impossible 
with heavy ones without more elaborate apparatus. The chains 
were almost all machine-made, as the weigntper unit of length 
is much more uniform in machine- than in nand-made ones ; 
their motion is therefore much more regular. They were 
generally of the common figure-8 pattern, one half of the link 
being at right angles to the other half. The chains of this kind 
varied in weight from 1^ oz. per yard to 10 oz. per yard ; other 
kinds of chains were also used, amongst them the pin and fiat- 
link chain used for hanging windows. 

For guiding and altering the shapes of the curves of the 
chains while in motion, wooden pulleys having grooves in their 
circumference, and running freely on steel spindles fixed to 
handles, were used. The shapes and sizes of these are shown at 
£, F, fig. 3. In some cases the hollow india-rubber ball 
shown at G, fig. 3, was found useful, not only for altering the 
shapes of the curves of the chain, but also for other purposes, 
which shall be described further on. The india-rubber ball 
was mounted on a steel spindle, by passing a brass tube through 
it, and fixing a circular brass plate to each end of the tube, and 
cementing we ball to.the end plates. The india-rubber ball did 
very well at first ; but as the chains require to be kept well 
oiled, the oil soon spoiled the india-rubber and made the ball 
nearly useless. The following plan was then adopted : — ^A fiange 
about 2-inch diameter was fixed to the end of a short piece of 
brass tube, and a loose fiange and nut was screwed on the other 
end ; disks of the required size were cut from sheet india^-rubber, 
and holes pierced in their centres ; the brass tube was passed 
through the centres of a sufficient number of these disks ; the 
loose fiange was then put on, and the whole screwed tightly 
up by means of the nut. This plan was adopted because the 
india-rubber could be easily and quickly replaced if destroyed. 
In place of india-rubber we may use disks of cloth. At first 
sight the pulley so constructed does not look very promising ; 
but after it is in use, the motion confers a quasi-eiasticity upon 
it which enables it to do its work remarkably well. 

For experiments with long chains the apparatus shown at 
fiff. 4 was used. It is simply a short steel spindle, to one end 
of which a small pulley, a, is fixed, and to the other end the 
wooden pulley H ; the spindle bearings are fixed to a piece of 



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88 Mr. J. Aitken on some Ea^erimenU on 

wood, c. The whole apparatus is firmly attached to a scaffolding, 
or any other convenient place, by means of screw-nails passing 
through e. The chain to be experimented on is hung over the 
pulley H ; and an endless cord is passed over the pulley a and 
carried down to the driving-wheel of the apparatus shown in 
fig. 1, which may be standing on a table or other convenient 
place. 

For experiments with a horizontal chain, a slight addition 
was made to the apparatus shown in fig. 1. These additions 
are shown in fig. 5. As before, a is the steel spindle, having 
the small brass pulley d fixed at one end, by wnich motion is 
communicated to it ; to the other end is fixed a wooden pulley 
c, having a groove in its circumference, in which is placed a 
stretched india-rubber band of circular section ; on the top of 
the pulley c rests the horizontal pulley «. Motion is communi- 
cated to the horizontal pulley t by means of the pulley c. The 
pulley % is supported in its position by means of the horizontal 
oars e e (only one of which is shown in sketch), which are 
clamped to the triangular supports hhhy means of the screws 
//• The horizontal bars e e are held together at the end by 
means of the cross-piece ^, to which they are held by means 
of the screws h h. To the cross-piece g is clamped, by means 
of the screw i, the vertical bar of wood m ; to m is attached, by 
means of the brass plate p^ the tube o, in which runs the spindle 
of the pulley % ; the brass plate p moves in m round the screw 
q like a compass-joint. By this arrangement the pulley t may 
be fixed in a horizontal position, or turned to any angle that 
may be desired, by first turning p round the screw 9, then 
lowering the bar m till the pulley treats on the pulley c. The 
horizontal bars e e rest on pins, uuuu, driven into b b. The 
bars ee can be moved on the pins uuuu to the right or 
left, so as to cause the pullev c to act near the centre or the 
circumference of the underside of the pulley t, so as to give 
a quick or slow motion to the pulley t, as may be desired for 
the experiment, r is an india-rubber ball mounted on a steel 
spindle, and so arranged that it can be adjusted to press the 
chain against the pulley t, at whatever angle the pulley i is put. 
In order to increase the friction between the pulley / and the 
chain, the pulley is covered with india-rubber. The pulley t is 

f)ressed against the pulley c by means of a spiral spring at the 
ower end of the spindle ; the spindle o is carried down below 
the horizontal bars e e for making experiments with apparatus 
hung from it. As all the bolts are provided with thumb- 
8crew8,the whole apparatus is easily and quickly taken to pieces. 
In addition to the apparatus shown in PI. lY., a simple ar- 
Cangement was placed below the pulley A, fig. 1, for guiding 



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Higidity produced by Centrifugal Force* 89 

the chain to the groove in the pulley ; also an arrangement for 
fixiBg an india-rubber pulley m a position to press the chain 
against the pulley A : they were held in position by being 
clamped to uie supports b b. 

Description of Experiments. 

I. If a long endless elastic band or cord is hung over the 
pulley fixed to the end of the spindle a, fig. 1, PL lY,, and 
motion is gradually communicatea to the band, the elastic band 
is seen to grow in length, the lower end of the loop getting 
further and further from the pulley, the loop keeping, however, 
much the same shape it had while at rest. This elongation 
becomes very marked if tlie band is loaded : if, for instance, 
we use an endless india-rubber band to which are cemented by 
means of india-rubber solution a number of pieces of leaa. 
This band, if put in motion (taking care to keep the pieces of 
lead on the inside of the loop to prevent them being torn off 
by the centrifugal force), can be easily drawn out to double 
its ori^nal length. 

II. If in place of an elastic band we hang an endless chain 
over the pmley and put it in motion, we ^ready know that 
the motion so communicated to the chain has but little ten- 
dency to alter the form of the loop in which the chain hangs. 
In fig. 3, PL III., is represented the change produced by uie 
motion in the shape of the loop : the full Imes show the form 
while at rest ; the dotted lines represent the shape when in 
motion. It will be observed that tne change is not great; and 
this is the case even when the velocity is great. Later on I 
shall show how the motion produces this change of shape. The 
motion will of course produce a tension in the chain similar to 
that produced in the india-rubber band ; but the chain, being 
much less elastic, is not elongated to any perceptible extent. 
If we now attempt to alter the form of the loop m which the 
chain hangs, we shall find that the motion has communicated 
new properties to the chain: it now resists any effort made to 
alter its shape ; and after we remove the disturbinfi" force gravi- 
tation can only very slowly restore it to its ori^nal form. The 
chain now conducts itself something like a rigid body. When 
struck near its lowest part, it looks like a bar of lead ; it be- 
comes indented at the point struck, and very slowly loses the 
impression of the blow. 

It has been customary to call this property which the chain 
has acquired in virtue of its motion hy the name of rigidity. 
There are, however, reasons which have induced me slightly 
to differ from the ideas generally received on this subject; and 
it is with the greatest diffidence that I here venture to state 



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90 Mr. J. Aitken on same EaperimenU an 

them, as the subject is one of great difficulty^ and one of which 
we have a very limited knowledge. A rigid body is one which 
is generally supposed to be capable of resisting a certain amount 
of force without being permanently put out of shape. The 
force required to put it permanently out of shape may oe small ; 
yet it is a perfectly definite amount. Now the chain, when in 
motion, may have its shape altered by any force, however small, 
the greater force only making the alteration take place more 

auickly. This being the case, does not this new property in 
lie chain correspond more to plasticity or viscosity than to 
rigidity ? Does it not conduct itself more like a piece of wax 
or a mass of treacle or tar than like a piece of lead ? Of course 
I am here using the word rigidity in its extreme sense, a sense 
in which perhaps no solid can be accurately said to possess it. 
Eigidity ana viscosity as applied to matter can perhaps 
scarcely be called different things, but may be more properly 
called degrees in the same scale, the scale beginning in perfect 
fluidity, passing through viscosity and plasticity to perfect 
rigidity ; but no substance with which we are acquainted has 
properties corresponding with either extreme end of the scale. 

III. In all the experiments, gravitation acts on the chains 
while in motion. Tne next experiments are to illustrate the 
manner in which gravitation acts on the moving chain and 
changes its form. When the chain is hanging from the 
driving-pulley, gravitation is balanced by the tension in the 
chain, and there is equilibrium ; but suppose now that the lower 
end of the loop is raised to one side of the driving-pulley, as 
shown in figs. 4 and 5, PI. III. The chain can easily be put 
into this position by means of the movable pulley E, fig. 3, 
PL IV. When the movable pulley is removed, and the cnain 
is only supported by the driving-pulley A, then the tension no 
longer balances the gravitation, and the form of the loop is 
changed. The chain does not keep its form, and swing as 
a solid body or as a chain not in motion would do, so as to 
bring its centre of gravity under the driving-pulley, but the 
chain in falling to a position of equilibrium passes through a 
beautiful series of curves. The forms which the chain passes 
through depend on the direction of motion of the chain rela- 
tively to the driving or supporting pulley. If, for instance, 
the upper part of the chain is moving towards A the driving- 
pulley, then the chain in falling to its position of equilibrium 
passes through a series of forms, a few of the intermediate 
shapes of which are represented in fig. 4, PI. III., and finally 
arrives at its position and form of equilibrium similar to that 
shown in fig. 3, PI. III. If, however, the direction of motion is 
the opposite of this, and the upper part of the chain is moving 



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Biffidify produced by Centrifugal Force. 91 

in a direction away from the drivinff^piilleyy then the diain 
passes through a series of shapes sacn as inose shown in fig. 
bj PI. lU.y after which the chain again falls through a series 
of forms similar to those shown in fig. 4, PI. III., before it ar- 
rires at its position of equilibrium fig. 3, PI. III., because the 
upper part of the chain in fig. 5, PL III., is now approaching 
the driving or suspending pulley. 

The reason for these difierent series of forms in the two 
cases is very simple. Take the case represented in fig. 4, 
PI. III. Here the links, where they leave the underside of the 
pulley, begin to be acted on by gravitation ; but as they are 
movinff rapidly, gravitation only acts a short time on them ; 
their (K)wnward motion is therefore very slow. As the links 
move further and further from this point, gravitation has had a 
fenger and longer time to act on them, so uiat their downward 
motion becomes quicker and quicker ; and therefore the links as 
they approach the driving-pulley are falling quicker than those 
leaving it — ^the result of which is, the chain in falling passes 
throng a series of forms such as those represented in fig. 4, 
PL in. Similar reasoning applies to the case represented in 
fig. 5, PL III. 

IV. We have shown by means of the diagrams figs. 1 and 2, 
PL III., that the tension just balances the centrifugal force at 
all points, and that therefore the chain has no tendency to 
change the shape in which it is moving. The next experi- 
ments (figs. 1 to 5, PL y.) show how this equilibrium may 
be destroyed, and also the effect of destroying it. A short 
endless chain forming a loop about 20 inches long is hung 
over the driving-pulley A, fig. 1, PL IV.; and the lower end of 
the chain, instead of hanging free, is allowed to rest on the 
platform R, fig. 1, PL V. When the chain is now put in 
motion there is no tension at the lower part of the loop, due to 
centrifugal force, because the downward motion of the links 
is now destroyed by striking the platform R; and there is but 
little tension on the descending side of the loop, and the 
tension on the ascending side is due to putting tne links in 
motion in an upward direction. As the velocity of the chain 
increases, the centrifugal force of the part of the chain resting 
on the driving-pulley being unbalanced by the centrifugid 
force at the lower end, the diain tends to rise off the pulley — 
the result of which is, the weight of the chain is gradually 
taken off the pulley ; and as this diminishes the friction be- 
tween the chain and the pulley, a limit in the velocity of the 
chain is soon reached, beyond which it is impossible to drive 
the chain, however quickly the pulley is driven. The chain acts 
in the opposite way, but with a similar result, to a self-acting 



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9i Mr. J. Aitken on same Experiments an 

break. In order^ therefore^ to cause the chain to take up the 
same velocity as tiie pulley, it was pressed aminst it by means of 
the elastic pulley G, fig. 3, PL I V ., with me following results. 

A. Fig. 1, Pi. Y., shows the effect when the chain is pressed 
by G at a, on the descending side, at the point where it leaves 
the pulley. There is no alteration in the path of the chain, 
because the chain after it leaves the pulley is moving in a 
straight line, and as there is no deviating force there is no 
centrifugal force, and therefore removing the tension in the 
chain has no effect on the direction of motion of the links. 

B. Fig. 2, PL v., shows the effect when the chain is pressed 
at the point p, a Utile higher up the pulley on the descending 
side. In this case, the centrifugal force of the curved part of 
the chain resting on op on the descending side of ihe pulley 
being unbalanced by the tension, the chain rises from the pulley 
and is shot away from it, as shown — ^the direction of its 
motion where it leaves the pulley being a tangent to the pulley 
at the point j9, where it is pressed by the elastic pulley G. Of 
course the curved part of the chain p q^ resting on the ascend- 
ing side of the pulley A, also tends to rise, but is kept in its 
place by the tension produced by putting the chain in motion 
after being stopped by the platform. 

0. Fig. 3, rl. v., shows the effect of pressing the chain at 
q on the ascending side of the pulley. The centrifugal force 
of the curved part of the chain resting on op q being un- 
balanced by the tension, the chain rises up off the pulley in an 
irregular curve, and only touches the pulley at tne point q. 
When the velocity is sufficient to cause the chain to rise up 
to such a height that all the slack chain resting on the plat- 
form R is taken up, then the conditions become altered. 
When all the slack chain is taken up, then the centrifd^al force 
produces a tension in the lower part of the chain, and, unless 
we can keep increasing the velocity of the chain, it can no 
longer keep its elevated position, because the centrifugal force 
. is now balanced by the tension ; and as the irravitation is now 
unbalanced, it gradually flattens the curve, tul the chain again 
comes to bear on the top of the pulley, and spreads itself out 
on the platform. 

D. Fig. 4, PL V. At the beginning of the previous experi- 
ment, as there was no tension in the chain to balance the 
centrifugal force of the part of the chain resting on the pulley, 
the centrifugal force overcame the force of gravitation and 
caused the (Siain to rise into the air. After all the slack chain 
resting on the platform had been taken up, and a tension was 
produced in the chain by the centrifugal force, the centrifugal 
force of the upper part of the chain was balanced by the tension. 



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Uigidity produced by Cenirifiigal Force. 93 

and was no longer free to overcome the gravitation, and the 
chain began to fall. At this point its fall mav be stopped, or 
it may be caused to rise again, by destroying the tension at the 
lower part of the chain. This we can do m two ways. We 
may either cause the chain to strike the platform as nearly as 
possible at right angles, as shown at fig. 4 ; the motion of 
the links will thereby be partially destroyed, and the tension 
at the lower part thereby reduced, and the chain will again 
rise ; or, if when the chain is meeting the platform at an acute 
angle, and the upper part of the chain is falling, we turn the 
platform so as to cause the chain to meet it at a less acute 
angle, then the chain will again rise ; or we may reverse the 
experiment. Suppose that while the chain is meeting the 
platform at right angles, as shown at fig. 4, and is keeping its 
elevated position, we bend the platform, as shown nt K^, so as 
to cause the chain to meet the platform at an acute angle ; 
then the chain at once begins to fall in the manner shown by 
the dotted lines, fig. 4. But so long as it keeps the form 
shown in full lines, fig. 4, it will keep balanced in its elevated 
position, for a long time standing on the platform B and onlv 
touching the pulley A at the point ^, — ^the reason for this 
being that, if we partially stop the motion of the links by 
causing them to strike the platform, or if we partially alter 
the direction of their motion by causing them to strike the 
platform at such an angle as partly to change the direction of 
their motion, then there will be less tension in the lower part 
of the chain than in the upper, as the tension in the lower part 
will be only that due to partially changing the direction of the 
motion of the links. 

In fig. 3, PI. v., the chain meets the platform at a very 
acute an^le, and the change in the direction of the motion of 
the links is almost entirely effected by the tension in the chain^ 
and only to a very small extent by the platform ; there is 
therefore not sufBcient unbalanced centrifugal force at the 
upper part of the chain to keep it in its ekvated position. 
But the case is different in fig. 4. In this case the platform 
assists in altering the direction of the motion of the links at 
the lower part, and the difference between ^he tensions in the 
upper and lower parts is sufficient to keep the chain in its 
elevated position against the force of gravitation. 

A chain forming a loop of 4 or 5 feet may easily be kept in 
the air for any length of time, as it tends to strike the plat- 
form nearly at right angles, as shown at fig. 5, Pl.V . If the velo- 
city of the chain is not sufficient to raise all the chain from the 
platform, then the apparatus under these circumstances is 
working something like a fountain, in which the driving* 



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94 Mr. J. Aitken on some ExperimenU on 

wheel is performing the part of a pump, and the loose chain 
on the platform the part of the water sapplj. The different 
parts of the jet, however, in this case are rigidly connected 
and all moving at the same velocity, which causes the curve 
of the chain to differ from that of the water jet. 

y. The chains in the previous experiments were, to a 
certain, degree, riffid. If we give the platform a quick up- 
ward motion, the cnain rises from the platform like a rigid 
body, and again falls on it, getting its form but little put out 
of shape by the treatment — because when it faUs on the 
platform, dthough it gets slightly flattened, yet it tends to 
bend so as to cause the links to strike the platform more 
nearly at right angles, and therefore tends to cause the upper 
part of the chain to rise again, till the chain is pulled upwards 
and into such a shape as to reduce the angle at which the links 
meet the platform, the chain thus again regaining its form 
of equilibrium. This quasi -rigidity communicated to the chains 
by the motion is so great, that when thrown off the pulley in 
rapid motion they run aJong the ground like wheels. The 
simplest way of making this experiment is to hang the chain 
over a pulley which has a flange on one side only, such as 
that shown at B, fig. 2, PI. IV. After sufiicient velocity has 
been communicated to the chain, it is easily slipped over the 
edge of the pulley and dropped on a platform, along which it 
will run for some distance. The platform ought to be movable, 
and should be brought as near the lower part of the chain as 
possible, as the chain gets put out of shape if it falls far. It is 
also an advantage to put some rough or ridged surface on the 
platform where the chain drops on it, as it enables the chain 
to get up a longitudinal motion quickly. 

The chains for this experiment may be short, so that when 
hung over the pulley they form nearly circular loops ; or they 
may be long, so as to form long loops. These long loops do not 
run along like a solid body, but always keep the longer axis 
of their figure vertical, as shown at D, fig. 6, Pl.V. As they 
move along they gradually lose their velocity, and get flattened 
down and put out of shape. For this experiment we may use 
light or heavy chains. Chains weighing from 6 to 8 oz. per 
yard do very well ; but any weight of chain may be used. A 
common watch-guard, for instance, if hung over an 8-inch 
pulley so as to form a loop 8 inches by about 2 feet, and driven 
at a great velocity, will, when dropped off the pulley, glide 
along looking like a polished wire hoop. It is not simply the 
'^ rigidity " which enables these chain-wheels to keep their 
shape and elevated position ; the explanation given in ex- 
periment IV. D also applies to them. 



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Rigidity produced by Centrifugal Force. 95 

A variation of this experiment may be made by dropping 
the chains when in rapid motion on an inclined metal or other 
polished sarface, where they will remain in rapid motion for 
some time, gradually getting their form flattened by gravi- 
tation. 

YI. The next experiments are best made with a long chain 
forming a loop of JO or 12 feet, figs. 1 to 4, PL VL The 
chain is put in motion by means of the pulley H shown at 
fig. 4, PL IV. 

A. Fig. 1, PL VI. If the chain is struck on the descending 
side of the loop (at, sav, the point B), then one part of the wave 
so formed is carried rapialy with the motion of the chain 
down the one side of the loop and up the other — ^so rapidly that 
the eye cannot follow it. After the wave strikes the pulley 
on the ascending side at C, it is reflected from it, and travels 
slowly down the ascending side of the loop G D, gradually 
becoming smaller and smaller, and dies out before reaching 
the bottom D. The other part of the wave which was formea 
when the chain was struck at B, slowly travels upwards 
against the motion of the chain, till it meets the pulley, when 
it is reflected, and very rapidly carried round by D to C, 
where, like the first part of the wave, it is reflected and slowly 
travels downwards. 

B. If we strike the chain on the ascending side at a point a 
short distance below C, so as to form the wave shown in fig. 1, 
PL VL, then the one part of the wave slowly travels down 
the chain, while the other part is rapidly carried up to the 
pulley, where it is reflected, and slowly travels down the chain ; 
and as this reflected wave travels more rapidly than the wave 
in front of it — on account of the greater tension on the chain, 
due to gravity, at the wave further up the chain — ^it overtakes 
the first wave, and the two form one complete wave, and travel 
to the bottom together. The successive positions and forms 
of the waves are represented by the dotted lines in fig. 1. 

C. The next experiment illustrates the manner in which 
gravitation acts on the moving chain. By means of the 
movable pulleys E and F, fig. 3, PL IV., the chain is put into 
the shape represented in fig. 2, PL VI., where H is the drj^ing- 
puUey and E and F are the two movable pulleys. The chain is 
then put in rapid motion in this shape, in the direction shown 
by the arrows. If now the pulleys E and F are suddenly 
removed so that all the weight of the chain hangs from H, 
the chain in falling passes through a series of forms somewhat 
like those represented in the figure. The points most worthy 
of notice in this experiment are : — 1st, the slowness of the 
descent of the co form ; 2nd, the peculiar balance of the chain : 



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96 Mr. J. Aitken on some Experiments 07i 

the chain does not swing as a solid body or chain not in 
motion woald do^ so as to bring the centre of gravity nnder 
the suspending pulley H ; but me descending side keeps the 
same position it had before E and F were removed, and the 
CO form alone slowly descends, its shape altering as it falls. 
The explanation given of experiment III. is also applicable to 
this case. The peculiar balance of the chain in this experi- 
ment reminds one slightly of the balance of the gyroscope. 
3rd. At the moment the pulleys E and F are removea a quasi- 
elasticity may be observed : the chain falls rapidly for a short 
distance, then stops and rises a little, and tnen falls again, 
making two or three vortical oscillations before it settles into 
a steady descent. The oscillations are probably caused by the 
unbalanced tension, due to the weight of the chain, on the 
pulleys E and F, adjusting itself to the new conditions after 
the pulleys have been removed. 

D. In making the next experiment, the chain while at rest 
is passed round the pulley E, in the manner shown in fig. 3, 
PL VI., so as to form a circular loop near the top on the 
ascending side of the chain. The chain is then put in motion 
by means of the driving-pulley H. After the chain has acquired 
su£Scient velocity the pulley E is removed, which is easily 
done by gently sb*iking the (main in front, just below the pulley 
E, and at the same time withdrawing the pulley. The loop 
E being now free, slowly moves down the chain, slightly in- 
creasing in size as it descends. Its successive positions are 
shown by the dotted lines. At first sight it might be thought 
that the descent of the loop E was entirely causedby its weignt 
Such, however, is not the case. The downward motion of the 
circular loop is a true wave motion ; and the velocity of its 
descent depends on the tension produced by the weight of the 
lower end of the chain. If we unfold the loop E, as shown 
at 0, we see at once that it is a wave motion, similar to that 
shon^n:! in fig. 2, PI. VI. This wave motion may still further 
be illustrated by making the circular loop on the dsscend- 
ing side of the chain, when the loop will ascend the chain. 
The upward motion on the descending side is not, however, so 
succQssftil, as the circular loop gets rapidly reduced in size, 
and only teavels a few feet before it is destroyed. This experi- 
ment may be varied in another way. We may put a movable 
pulley into the lower end of the loop at D, so as to enable us to 
mcrease the tension in the chain, when we shall find that by 
increasing the tension we can cause the circular loop to move 
faster, in accordance with the laws of wave motion. 

E. The last experiment with this chain to which we need 
refer is made in the following manner. The chain is put in 



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Rigidity produced by Centrifugal Forte. 97 

motion in the sliape shown in fi& 4, PI. VL, by means of the 
movable pulleys E and F. I^ while the pulley E is kept 
steady, a downward motion is given to thepnllej F, the chain, 
mstead of pressing harder on me pulley E, rises quite off it, 
as shown in the dotted lines in the figure ; and if the down- 
ward motion of F be continued, the circular part which 
formerly rested on E rises till it strikes the driving-pulley H. 
The downward motion of F requires to be quick at first ; but 
after the chain begins to rise a very slow motion is all that is 
neoessaxy. The reason for the chain rising from the pulley E 
is, that the downward motion of the pulley F increases the 
velocity of the chain at ^r ; therefore the centrifugal force of 
the part of the chain resting on E is increased, while the 
centrifngal force at % is not increased. The chain therefore 
yields at s and rises at r. 

This change in the shape of the chain is perhaps easiest 
studied in a chain not in motion, but simply fixed at one end, 
the other end hanging free. If we hang the lower end of the 
chain over the pulley E, as in fig. 4, PL VL, and pull the free 
end of the chain at F, we get a similar result to what we get 
when the diain is in rapid motion. But in this case the down- 
ward motion of the end of the chain must be much quicker ; 
and the upward motion of the curved part ^^ r is correspond- 
ingly qnick — so quick that the eye can scarcely follow it. 
Wnen we pall the free end of the chain at F we thereby give 
the diain at ear slr upward motion. Suppose that we stop 
pulling at F after the chain has acquired a motion sufiiciently 
quick to enable it to rise off the pulley E. The curved part 
will form a regular wave motion, the links at a being in rapid 
upward motion, while those at r are gradually losing their 
motion, the energy of their motion being transmitted by the 
chain at a to put the links in motion at s. It is very evident 
that all the energy lost at the last part of the wave at r is not 
spent in putting the links in motion at the beginning of the 
wave at «, but has to do work against the force of gravitation — 
because if the energy were simply transferred from r to «, as 
in many wave-forms, then the* wave ear might travel up 
any length of chain, and in so doing lift the whole chain the 
height s r, when the energy put into the part sqr was only 
sufficient to raise the part sqr to r. To enable the wave to 
travel up the chain we must communicate energy to it while 
in motion, by keeping up a tension at the lower end of the 
chain at F. The end of the chain must therefore yield to the 
tension, and the part sqr become less and less as it travels 
up the chain. 

The wave-forms represented in figs. 1, 3 and 4, PL VI., 
PhU. Mag. S. 5. Vol. 5. No. 29. Feb. 1878. H 

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98 Mr. J. Aitken on some Experiments on 

move very slowly, on account of the motion of the chain; and 
if we attempt to make the experiments with a chain not in 
motion, the waves travel so qnickly that the eye cannot 
foUow them. If we could rednce the tension in the chain doe 
to its weight, then the waves would travel slowly, even in a 
chain not in motion. The simplest method of doing this is 
to lay a length of chain on a horizontal polished surface ; in 
the absence of a better, a wooden floor will do. One end of 
the chain is fixed ; the other end is then, by means of the hand, 
caused to take any of these wave-forms. When this is pro<- 

ferly done the wave travels along a great length of chain, 
n making this experiment the most important point to be 
attended to is not to bring the hand to rest after the wave is 
started. Hie hand with the end of the chain must be gradually 
and steadily withdrawn, so as to keep up a slight tension in the 
chain ; otherwise the wave will travel but a short distance. In 
making the experiments in this way, as the tension in the 
chain is small, the waves move so slowly that they can easily 
be followed with the eye. Beside the wave-forms mentioned , 
the chain may be made to take up any others that may be 
desired ; and the waves may be put in motion either in a hori- 
zontal or vertical plane. 

YII. All these experiments only illustrate the balance of 
the centrifugal force and the tension when the motion is con- 
fined to one plane. The next experiment is to show that these 
forces are also in equilibrium when the motion is not confined 
to any plane, but is constantly changing from one plane to 
another. In order to illustrate this we can take either the 
short or long chain used in the previous experiments, and, by 
means of the mov.ible pulleys, bend the lower part of it, while 
in motion, into a plane at right angles or at any angle to the 
plane of motion of the upper part, when we shall find that, 
though gravitation slowly unbends the chain, the centrifugal 
force has no tendency to alter its shape. This point, however, 
may be illustrated in another and better way, if we take a 
circular disk of paper, or any other flexible material (A, fig. 1, 
PL VII.), and mount it on the apparatus fig. 1, PI. IV., so that 
it can be rotated round its centre ; this is easily done by cut- 
ting a hole in the centre of the disk and fitting it to the 
arrangement c at the end of the spindle a. 

Let us first see what the result is if we Jlrst bend the disk 
and then put it in motion. The results may be summed up 
under three heads : Ist, the bent part rotates with the disk ; 
2nd, the centrifugal force tends to unbend the disk; and, 3rd, 
the elasticity of toe disk also tends to restore it to its original 
shape. If now yvQ first put the disk in motion and then bend 



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Rigidity produced by Centrifugal Force, 99 

it to the form shown at B^ fig. 1, PL YII.^ we get qaite a dif- 
ferent set of resaltfi : Ist, the bent part does not rotate with 
the disk, but keeps its original position, if the motion of the 
disk is kept uniform ; if the speed is either increasing or 
decreasing, the bend will go very slowly either forwards or 
backwards ; 2nd, there is no centrifugal force tending to 
unbend the disk ; and, 3rd, the elasticity of the disk only very 
slowly restores it to its original form, as it is resisted by the 
rigidity prodaced by the motion. 

Although a disk of paper illustrates these points, yet the 
experiment is much improved by loading the circumference of 
the disk, as this increases its rigidity without increasing its 
statical stiffness. The disks used in the experiments were 
about 18 inches in diameter, made of cartridge drawing-paper. 
The circumference was loaded with flatten^ pellets of shot 
placed about f inch apart, and fixed to the disk by means of a 
strong solution of india-rubber. If the weight added to the 
disk is such that it just balances the elasticity of the paper, 
then the bend remains in the same place, and the disk keeps 
the same shape for a very long time, while the disk is rotating 
rapidly. The disk may be bent till the circumference touches 
the centre (B, fig. 1, f*l. VII.) ; and while the bend keeps its 
position the chain of shot passes through many difierent 
planes ; and as the tension just balances the centrifugal force 
at all points, the disk has no tendency to alter its shape. 

The change in the form of the rotating disk will produce an 
alteration in the internal strains in the disk. When the disk 
or any other body, such as an ordinary fly-wheel, is rotating, 
the centrifugal force is resisted in two ways — ^partlv by radial 
tension, and partlv by tangential tension ; and the amount 
borne in each of these directions will depend on the relative 
elasticity of the material in the rim and in the spokes, and on 
the manner in which the wheel is constructed. The principal 
part of the strain may be borne by either the spokes or the 
rim of the wheel, as may be desired. In the paper disk, when 
its motion is all in one plane the strain will be borne in both 
ways, but when it is bent the strain will be almost entirely 
tangential. 

Before proceeding further it will be necessary for me to 
refer to some of the disturbing forces which I have already 
stated to be in action in the moving chain, tending to cause 
it to alter its shape. When looking at a chain hung over a 
pulley and in rapid motion, fig. 3, r\. III., the most marked 
eifect of the motion which we notice is a flattening of the curve 
of the chain, just before it begins to turn at the lowest point; 
and after the chain has turned and begun to ascend, there is a 

H2 

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100 Mr. J. Aitken on same Experivients on 

cnrions reverse curve in the chain, caused by it carving fiirther 
round than seems necessary, and then requiring to be unbent 
again. These two alterations in the shape of the loop look as 
it the motion had conferred a certain degree of rigidity on 
the chain, which enabled it to resist bending at the entrance to 
the curve, and also to resist unbending at the other side. 
There are also alterations in the shape of the loop near the 
driving-pulley. It will be also noticed that the diain does 
not now hang in the same position as when at rest ; its centre 
of gravity is evidently a little to one side of its position 
of rest. This is caused by the manner in which motion is 
imparted to the chain ; the tension on the ascending side 
of the chain is greater than on the other side, thus causing 
the centre of ffravitjr to move to the one side. 

y III. The alterations in the curvature of the chain produced 
by the motion have hitherto been supposed to be due to the 
friction of the links pivoting on each other, under the great 
tension produced in the chains by the centrifugal force. That 
this is not the full explanation, however — uiough it may, 
in part J explain the flattening of the loop at the entrance to 
the curve — ^is easily proved by taking two precisely similar 
chains, and passing one of them through a flame, so as to dry 
and oxidize its suriace, and oiling the other chain. The only 
difference between the two chains now is, that there is more 
friction in the one than in the other when in motion. If we 
now hang these two chains over the double pulley C, fig. 2, 
PI. IV., me two gooves in which are of exactly the same 
diameter, so as to drive the two chains at the same velocity, 
we shall thus get what the effect due to friction is. We find 
that the oiled chain has the reverse curve well marked, while 
there is no reverse curve in the other chain, the effect of the 
friction being to make the loop open out and take up a form 
approaching a circle. Further, if we cause both of the chains 
to take up the same curvature at the bottom part of their paths, 
which we can easily do bv passing them over a small pulley 
or a glass rod, we shall then find that the reverse curve is 
notably least where the friction is greatest. 

The alterations in the curvature of the chain when in motion 
are in all probability almost entirely due to the change of mo- 
tion which takes place in the links when moving in a path of 
varying curvature. For instance, when a link is oescending the 
flat part of its path (a, fig. 3, PI. III.\ its motion is almost 
simply one of translation ; whereas, wnen moving round the 
curved parts, such as 6, it has a motion of rotation as well as a 
motion of translation. The result of this is, the links resist the 
force tending to increase their rate of rotation when passing from 



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Rigidity produced by Centrifugal Force. 101 

a path of slower to a path of qaicker carvatare, and after tha 
rotation has been imparted to the links they tend to keep np 
their rate of rotation, and thus oontinae the carve mach far- 
ther round than if the chain were not in motion. If the chain 
were infinitely thin, this woald not be the case. The part of 
the links in the line of tension has no sach tendency ; it is 
the parts of the links on the inside and outside of this line 
f^ch produce the result. 

The outside of the curve of the chain, when passing from a 
straight path to a curved one, is moving too slow, and we inside 
too quicK, to pass round the curve ; the chain therefore resists 
benmng ; ana after the outside of the curve has acquired in- 
creased velocity and the inside lost it, the chain cannot move 
in a straight path till the inside and outside parts have again 
acquired the same velocity. The different velocities of the 
outside and the inside of the loop in passing round a curve 
therefore cause the chain to continue to curve farther round 
than it would do if not in motion. This tendency to cause the 
chain to continue curving further round would cause the chain 
to deviate further from its original shape if it were not resisted 
by the tension produced by gravitation. This varying rota- 
tion also explains why the quickest part of the curve is not at 
the lowest part of the path of the chain, but at a short distance 
up the ascending side of the chain. The links at the lowest 
point are still acquiring an increased rate of rotation ; and it 
is not till past this point that they acquire their maximum 
rate. 

IX. These points may be illustrated by a chain in which 
the links are short and the chain thick, so that the moment 
of inertia of the links round an axis perpendicular to the plane 
of motion of the links is as great as possible, and the moment 
of the tension round this same axis as small as possible. A 
simple method of constructing such an experimental chain is to 
fix by means of glue a series of pieces of wood about 1 inch 
long and of the section shown in fig. 2, PL YII., on each side 
of a strong piece of tape about 1 inch broad. When this 
chain is hung over the pulley D (fig. 2, PL lY.) and put in 
motion, the reverse curve is very marked (fig. 3, PL VII.). So 
great is the effect of the varying rate of rotation of the links 
m this chain, that they never take up a steady motion of trans- 
lation ; the links are constantly rotating too quickly the one 
way or the other, which gives rise to the well-marked series of 
waves all the way up one side of the loop and down the 
other. 

At A and B (fi^. 4, PL YII.) I have shown what I suppose 
to be the manner m which the varying rate of rotation oi the 



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102 Mr. J. Aitken on some Expeinments on 

links alters the form of the curves ; A shows how the flatten- 
ing is produced at the entrance to the curves. Suppose the 
link 1 to be moving in a straight path and just entering on 
the curve cd, the links 2, 3, &c. have entered the curve. The 
sketch shows the position of the links with regard to the line 
of tension. The anks tend to keep their centre line vertical, 
and resist moving in the curved line c d. The sketch also 
shows that, by doing so, in passing round the curve the ten- 
sion on each end of the link is no longer in a straight line, 
but acts as a " couple," tending to cause the link to rotate. 
Again, B shows the effect of the rotation of the links when 
passing from a curved into a straight path; the link 1 is 
moving in the curved path c d. The outer parts of the links 
are in this case moving quicker than the inner, the result 
of which is to throw the centre line of the link inwards, 
thus causing the link to move inwards, and also forcing the 
link in front inwards, so causing the links to continue to move 
in their curved course. This rotation of the links causes the 
tension in the chain to act as a " couple " on the links as 
shown, but this time in the opposite direction to the case A, 
and tends to destroy the rotation. But before the rotation is 
destroyed, the chain has curved far past its position of rest ; 
the links have therefore to come back again, and in doing so 
have a rotation in the opposite direction given them, which 
again causes them to overshoot the mark, from which they 
have to be brought back ; and thus, by a continued series of 
rotations in one direction and then in the other, the well- 
marked waves shown in the figure are produced. 

We may, by altering the shape of the links, get still more 
marked effects — ^if, for instance, instead of placing the pieces 
of wood on both sides of the tape we place the same size of 
link all on one side, so that the vmole weight of the links shall 
be on the one side of the line of tension. This form of chain, 
however, is not so steady in its motion as the other one. If, 
for instance, we place the tape, that is tiie line of tension, on 
the outside of the curve, then the form becomes extremely 
unsteady. If the two sides of the chain do not take exactly 
the same curvature, the side with the most curvature tends to 
turn round the other one, and the chain, if its construction 
admits of it, turns itself inside out, so placing the line of ten- 
sion inside the loop. 

X. The length of the links has also an influence on the cur- 
vature which the chain will assume when in motion. If we 
make two chains of exactly the same size and kind of wire, so 
that they shall be exactly alike in every respect except the 
length of links, when these two chains are hung over the 



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Rigidity produced by Ceiitnfugal Force. 103 

pnlley C (fig. 2, PI. IV.) and driven at the same velocity, the 
loop of the chain with the longest links opens out and tends 
to take up the circular form, the smaller links keeping near 
the form the chain had while at rest. In the long-link chain 
there is no reverse curve, while it is well-marked in the short- 
linked one. 

XI. An elastic cord in rapid motion also tends to assume 
the circular form, because tl^ internal strains in the quicklv 
curved parts tend te open them out in the same manner as if 
the cord were at rest An el^ticcord, when in motion, dors 
not take the reverse curve like a chain, because its tendency 
to do so is resisted by the strain in the material. 

XIL In mil these experiments gravitation acted on the 
chains, so that, whatever form we might give them, gravita- 
tion soon restored them te their original form of stability. 
An attempt was therefore made to get quit of the disturbing 
effects of gravitation, as it was thought that the action of the 
other forces might be more conveniently studied if its effects 
were removed. The problem, however, is an extremely diiH- 
cnlt one, and has quite baffled all my attempts. Many me- 
thods suggested themselves for accomplishing this end ; some 
of them were tried ; but none of th?m was successful. The 
next experiment shows the plan which was found most suc- 
cessful, namely suspension. The chain n (fig. 5, PI* VII.) is 
suspended by a number of fine cords ddto2k circular metal 
disk e. The disk e rotates freely about a vertical axis, and is 
placed at a considerable distance above the chain n, so that 
the cords dd may be as long as possible. The disk is also 
capable of being moved in anv airection horizontally. In 
the experiment this was done by hanging it b}' means of a 
long wire. Motion was communicated te the cliain by means 
of the apparatus shown at fig. 5, PI. lY., the chain being 
passed round the horizontal driving-pulley i and pressed 
against it by means of the elastic pulley r. 

Let me here briefly refer to the impeifections of this arrange- 
ment, as the results are modified by these imperfections. 
First, the effects of gravitation are by no means balanced by 
this arrangement, as may at onoe be seen by the position of 
the cords. This imperfection may, however, be reduced by 
making the cords long, and by arranging the point of suspen- 
sion so that it can be moved in every direction, so that the centre 
of suspension may always be kept vertically over the centre of 
gravity of the chain. Second, the method of imparting 
motion to the chain is very imperfect. The chain ought to 
be perfectly free at all points, whereas this method compels 
the chain always to pass between the two pulleys. And, third. 



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104 Mr. J. Aitken on some Experiments on 

the force necessary to keep np the motion is imparted to the 
chain at one pointy which ouffht not to be^ as it produces a 
tension in the chain which vanes in amoimt at the different 
parts, being greatest at the part approaching the driving- 
pallej. These imperfections must sJways be borne in mind 
when experimenting with this apparatus. 

To set the chain m motion, it is first put romid the pnllev i 
and then tightened by holding it out by means of one of toe 
movable pulleys, in the form shown at fig. 6, PL VII. After the 
apparatus is set in motion, the movable pulley may be re- 
moved, as the centrifugal force tightens the chain. When in 
motion, we shall find tliat we can, by means of the movable 
pulleys, mould the chain into a variety of curves, and that it 
will retain for some time whatever shape we give it. We may 
also notice that it resists our efforts to alter its form, and that, 
after we have succeeded in altering fts form, the motion has 
but little tendency to change the shape of the curves. 

These are, however, onfy the general results which strike 
one at first. On more careful experimenting, the imperfeo- 
tions of the apparatus and the effect of the varying rate of 
rotation of the links become rery evident. If we continue 
the experiment for any length of time, we shall find that 
the chain slowly changes its shape when put into most 
forms, and that it is only stable in a ver^ few forms. If, 
for instance, the centre of suspension is kept over the 
centre of gravity of the chain, it will keep the circular form, 
or it will keep the form shown at fig. 7, PL YIL, though 
it will not keep the form shown at fig. 6, PL VII., because 
the chain tends to continue the bend at a on account of the 
rotation of the links. It keeps the form shown at fig. 7, 
PL VII., because the links are prevented from curving any fur- 
ther at a by the tension produced in the chain by tne pulley 
in keeping up its motion. The chain does not tend to curve 
inwards at b, partly on account of the pressure of the pulleys 
t and r on the chain tending to cause the links to leave the 
pulley t at the point of contact, and partly because there is 
less tension in the chain at b than at any other part, as the 
tension produced by keeping up the motion is least at this 
part. It is well to remember that the half of the chain next 
the pulley is so influenced bv the pulleys and difference in 
tension, tiiat it is difficult to draw conclusions from the action 
of the chain at this part. We may show tlie imperfections ^f 
the apparatus in another way. I^ for instance, tiie line drawn 
vertically through the point of suspension falls to one side of 
the centre of gravity of the chain, then the chain will keep an 
oblong shape; but if the point of suspension is graduaUy brought . 



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Rigidity produced by CentHfugal Force. 105 

over the centre of gravity of the chains then the form of the 
chain changes and approaches that of a circle, and the chain 
may again be made to take its original oblong form by moving 
the point of suspension to its original position. The circular 
form which the chain takes np vmen tne centre of sospension 
is kept over the centre of gravity is due to friction, length of 
Hnks, and other causes. 

The effect of the varying rate of rotation of the links on their 
own axis is also well marked, especially if we give the chain a 
quick curve at any point. The effect, however, is very dif- 
ferent from what we get when the chain is hung over the 
driving-pulley. When the chain is hung over the driving- 
pulley, tnere is a tension in the chain due to gravitation ; this 
tension, coupled with the rotation of the links, gives rise to 
the wave-form which we saw certain forms of chain took up 
when in motion, fig. 3, PL VII. The tension due to centrifugal 
force has no such effect. When, therefore, in this experiment 
the chain is suspended and the tension due to gravitation re- 
moved, there is but little tension preventing me chain from 
continuing to curve further in the same direction. The chain 
ilierefore goes on bending further and further round until it 
comes into collision with the part of the chain moving in the 
opposite direction, and stops the motion, even though the 
cnain at this point is bending out' of the way on account of 
the resistance offered by the links at this part to rotation on 
their axis. This effect is best shown by using a chain speci- 
ally prepared for showing the effect of the varying rate of ro- 
tation of the links, such as the one used in experiment IX. 

While these experiments illustrate the laws of motion, they 
also in a somewhat rough way illustrate certain early specu- 
lations on the structure of matter which have recently been 
revived and founded on a scientific basis. In these experi- 
ments, as in the well-known vortex-ring, motion confers cer- 
tain properties whidi we are in the habit of associating with 
fte solia condition of matter. This, however, is a subject 
alike beyond my province and my powers ; I must therefore 
take leave of it^ and conclude by expressing a hope that the 
experiments may be useful to those engaged in the higher and 
more difficult investigation of the subject. 

Danoch, Falkirk. 



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[ lOG ] 

XV. Short Reports from the Chemical Lahoratory of Trinity Col- 
legej Dublin. By J. Emerson-Rkynolds, M.D.y M.R.LA., 
Professor of Chemistry, University of Dublin*. 

No. 4. — On a New Form of Measurinff- Apparatus for a 
LaborcUory^Spectroscope t. 

THE measnring-apparatas for a laboratory-spectroscope 
which I have been asked to describe, was fitted about a 
year ago to an instrument in common use in the College La- 
boratory, and has afforded very satisfactory results. My chief 
aim in planning the arrangement was, to facilitate the measure- 
ment and identification of spectral lines and the mapping of 
spectra under circumstances admitting of little general illu- 
mination. 

The spectroscope to which the apparatus is fitt>ed has two 
fixed flint-glass prisms, the refracting angle of each being 60°. 
This instrument is shown in the annexed engraving. When 
in use the prisms are covered by a bi'ass cap provided with 
openings for the collimating- and observing-telescopes. The 
movable arm D that supports the observing-telescope also 
carries a vernier which is moved with the telescope over a 
graduated arc ; and in this usual way the relative positions of 
the several lines of a given spectrum can be determined. The 
angular distance traversed'in passing from the extreme red 
to extreme violet is necessarily small, owing to the low dis- 
persive power of the instrument 5 but this, I need scarcely say, 
is an advantage rather than the reverse in a spectroscope 
which is commonly employed as an aid in ordinary qualitative 
anaJ>'sis. 

The graduations of the arc are unavoidably close and diffi- 
cult to read in a feeble light ; consequently the eyes of the 
observer become speedily tired and unfitted for the examination 
of faint spectra. Nevertheless measurements made with the 
graduated arc and vernier are, in my experience, more trust- 
worthy and satisfactoiy than those obtained with even the best 
photographed scale that I have had the opportunity of working 
with. Desiring, then, to retain the method of direct angular 
measurement, I sought to multiply the motion in such a manner 
as to obtain wide readings on a convenient scale. After many 
trials in different directions, the form of apparatus which 1 
shall now describe was finally adopted. 

* From the Scientific Proceedings of the Royal Dublin Sociesy ; com- 
municated by the Author. 



t For Report No. 1, ** On Glucinum : its Atomic Weight and Specific 
[eat," see rhil. Mag. [V.J vol. iii. p. 38 ; for No. 2, On a New Mineral 
Borate, and for No. 3, On an Analysis of Lievrite by Mr. Early's Me- 



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MecLsuring- Apparatus for a Laboratory- Spectroscope. 107 

Description of t/ie Apparatus, — The annexed woodcut, which 
is taken from a photograph, represents the whole apparatus. 



The index A, attached to the spectroscope, moves in front of a 
graduated plate of opal glass, the latter being supported, in the 
manner shown, by the stand S*, to which the spectroscope is 
also screwed by means of the rod R. The index is attached to 
a milled head which moves stiffly on a stout steel rod r ; the 
latter can revolve in little bearings supported by the projecting 
arm of " angle-brass," a, the other end of the rod being lot 
into a hole drilled in the head of the pillar, P, of the instru- 
ment. On the rod just mentioned, and immediately beneath c, 
a small toothed wheel is securely keyed. The diameter of this 
wheel is about one centimetre, and the teeth upon it are fine 
and well cut. c is a stout metallic strip, five centimetres long, 
whose lower edge is serrated so as to correspond accurately 

* The stand is of stout walDut-wood. A rebate of the thickness of the 
glass plate is cut to the depth of three centimetres fiom the vertical piece 
of the stand. The straight edge of the plate is laid in the groove and is 
there secured, in part by a pin passing from behind through a hole drilled 
in the glass , and m part by a wooden slip screwed on in front. 



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108 Prof. J. Emerson-Reynolds on a New Form of 

with the teeth of the wheel on the rod r, and to act upon the 
teeth directly so as to cause the rod carrying the index, A, to 
rotate easily. This strip is bent to a curve whose radius is 
equal to the distance from the axis of the pillar, P, of the 
instrument to the middle of the toothed wheeL The strip is 
attached to a stout arm ; and this is in turn screwed to the 
slightly projecting end of the heavy plate, D, which carries, 
and of course moves with, the observing-telescope, the motion 
being communicated to the latter by turning the milled head 
m. As the observing^-telescope moves over the graduated arc 
gy the index A moves in front of the graduated plate B, but in 
the opposite direction; for the motion of D is communicated 
to the rod r by means of the serrat>ed slip c. When the fittings 
are well made, the movement of the index A is steady and 
corresponds in both directions with those of D. By the simple 
means described, a very slight motion of the observing-telescope 
produces a comparatively considerable displacement of the 
index A. 

In my instrument, the telescope and the index move in 
opposite directions. Any objection on this score can be re- 
moved ; for it is only necessary to point out that the motions 
may be made to coincide in direction by placing c under in- 
stead of over the toothed wheel. 

Graduation of the Glass Plate. — It is veiy desirable that the 
graduations on the plate and on the arc of the instrument 
should agree ; the best mode of securing this is to graduate 
the plate with the aid of the arc. For this purpose the tele- 
scope is moved into such a position that the rays less refrangible 
than the red potassium-line shall occupy the field of view ; 
the zero of the vernier is then made to coincide with the nearest 
convenient degree marked on the arc. The rod r is then firmly 
grasped and me index A brought down to a horizontal posi- 
tion, and a fine dot made on the plate under the point by 
means of a pen dipped in " black japan.." This point is taken 
as the zero of the scale. Each half-degree is marked off in 
a similar manner until the semicircle is graduated. The two 
scales are again compared at different points, and the opal- 
glass plate removed ; each large division, corresponding to 
half a degree, is tiien subdivided into 1 * equal parts. Finally 
the semicircle is numbered fi*om zero up to 200 : each division 
of the scale therefore corresponds to 3^ of the arc g. In my 
spectroscope the angular motion of the observing-telescope is 
magnified 25 times, and the width of each division of the glass 
scale is 2^ millimetres, so that the readings are easily made 
in a feeble light without straining the eyes of the observer. 
♦ In the woodcut only five Bubdivisions are shown. 



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Measuritiff''Apparatu8 for a Laboratory^Spectroacope. 109 

Reading cff PosUiona of Spectral Lines* — In commencing an 
observation it is always desirable to see tbat the point of the 
index A stands at the zero of the glass scale when the telescope 
18 in the corresponding position on its scale. Any adjustment 
of the index that may be necessary is easily made in the way 
already described — namely, by firmly holding the rod r and 
taming the milled head which carries the index to the desired 
extent. The actual reading of the position of a line to which 
the point of the fine needle in the eye-piece is brought is then 
made from the glass scale. 

An exceedingly feeble light suffices to enable the operator 
to read the wide divisions on the white scale ; but in observing 
very faint lines I do not read by reflected light, but faintly 
illuminate the scale by means of a very small gas-jet or lamp 
placed behind it. Sufficient light is transmitted by the opal 
glass to enable the readings to be easily and quickly made, 
while the eye of the operator is retained in a sensitive 
condition for feeble rays. Moreover, in reading, it is not 
necessary to move the nead away from the eyepiece of the 
instrument. 

I have tried with success a mode of determining small dif- 
ferences with this apparatus, which could doubtless be applied 
with advantage in mapping spectra with instruments of high 
dispersive power. 

The glass plate B was removed from its stand and the index 
from the rod r ; I then attached to the latter a cork carrying 
a small mirror placed at a suitable angle. A spot of light was 
reflected from this mirror and made to fall on a screen placed 
several metres away. The relative distances between the 
members of groups of closely ruled lines (those of the nitrogen 
spectrum) were tnen easilv determined in this manner, as the 
actual motion of the needle from point to point was greatly 
magnified. 

&e relative positions and widths of the lines seen with the 
instrument are easily laid down on a millimetric scale. I have 
had a number of 200-m.m. scales printed on narrow slips of 
paper ; and the graduations are lithographed on a band of six 
equidistant lines, which thus serve for marking off intensities, 
according to Bunsen's graphic method. One millimetre cor- 
responds to one unit of the scale on the opal-glass screen, and 
consequently to three minutes as read off with the vernier on 
the graduated arc of the instrument. Differences corresponding 
to r can therefore be easily estimated and represented on the 
millimetric scale. 

But one other practical point need be mentioned. I find it 
exceedingly convenient to mai*k off on the opal-glass scale the 



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110 Dr. 0. J. Lodge on a Method of measuring the 

positions of the more important lines of the elements whose 
spectra are easily obtained with the aid of the Bansen flame. 
The symbol of tiie element to which a particular line or band 
belongs is legibly written under the particular point of the 
scale, and connected by a line with the point in question. 
Identification of the bright lines observed in the spectrum of 
an unknown compound is thus greatly facilitated. 

I may be permitted to add that the measuring-apparatus 
described has been fitted to the spectroscope used in the College 
Laboratory by Messrs. Yeates and Son of this city, whom I 
have to thank for the care and skill with which they carried 
out the details of construction. 



XVI. On a AfetJiod of measuring the Absolute Thermal Con- 
ductivitg of Crystals and ot/ier rare Substances. — Part I. JBg 
Oliver J. Lodge, JJ.Sc* 

1. "TTT'HEN only a small portion of a substance is obtain- 
▼ ▼ able on which to experiment, the measure of con- 
ductivity by any dia-calorimetric method becomes diflScult; and 
accordingly observers have contented themselves, in the ciise of 
the rarer crystalline bodies, with comparing their conductivities 
in different directions by S^narmont's or some similar method. 
If the substance is sufficiently plentiful to be obtained in slabs 
(like rocks), then some modification of Fourier's "thermo- 
metre de contact" will give its conductivity, though there 
are many objections to the use of this instrument. 

But there is another method of Fourier's, applicable only to long 
rods, put in practice by Biot, Despretz, Forbes, and recently by 
Wiedemann and Franz (commonly known as Forbes's method), 
which it seems possible to modify so as to make it applicable 
to short rods or even slicesf. This well-known method consists 
in observing the permanent curve of temperature along a cy- 
lindrical rod of the given materiid, one end of which is neated 

♦ Communicated by the Physical Society. 

t The method oocunred to me when thinking how best to measure the 
conductivity of tourmaline in opposite directions along the axis, a subject 
which I was considering in conjunction with Mr. 8. P. Thompson of 
Bristol ; for we had reason to think that tourmaline and all other pyro- 
electric crystals must necessarily possess a unilateral conductivity along 
their axis both for heat and electricity ; and this supposition has been 
partially confirmed^ in the case of heat^ by some preliminary experiments 
of Mr. ^Thompson's last summer on a very small crystal. No further con- 
firmation or modification of the experiment, howeyer, has yet been pos- 
sible, owing to the pcarcity of the crystal and the difficulty of obtaining 
a large slice ; but this difficidty has now been removed by the kindness 
of Professor Nevil Story Maskelyne. 



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Absolute Thermal Conductivity of Crystals 8fc. Ill 

and the rest exposed to the atmosphere. Let s be the area of 
cro6s section (which need not be circular) and P the perimeter 
of the rod, the latter being defined as the length of a string 
wrapped once round the rod if the actual perimeter is any re- 
entrant curve. The condition to be expressed is that the total 
gain of heat of any element of the rod by its anterior, posterior, 
and exterior surfaces is equal to nothing. Taking t as the 
excess of temperature over that of the air of an element in a 
position X along the rod, we have the quantity of heat 

^1 dt entering at its anterior or hotter surface in unit 
""5^ time, 



■i« (^ + -T^da) at its posterior surface, 



— PA< dx at the surface exposed to the air ; 

k being the conductivity of the rod, and h the radiation-coeffi- 
cient of its surface, t. e. the quantity of heat lost in unit time 
by unit surface when it is one degree hotter than the air. 
Putting the sum of these quantities equal to zero, we have 

d^t PA^ - 
^ = _^=;>^^say, 

an equation whose complete integral is 

t^Gi^+Cie-P*, 
or, as I shall prefer to write it, 

^=A cosh par— B sinhjt?.r. 

The constants A and Bare determined in terms ofp as soon 
as one knows the temperatures of any two points of the rod ; 
and the temperature of a third point will determine jo, whence, 
if h be separately found, k is known. Thus, suppose we know 
t^ the temperature of the origin, and i^. the temperature of a 
point at a distance a from it, and also t^ the temperature half- 
way between these points ; then 

A^t„ 

B = ^Q coth^o? — t, cosech pjCy 

o= - cosh"*-^— *• 

2. Now suppose the rod to be cut in half and a slice of 
crystal or any substance interposed : the curve of temperature 
will have a discontinuity at the junctions ; but if the curve along 
each rod is observed, it may be possible to calculate it for the 
crystal. The method which I propose, then, is to cut a cylin- 
drical piece of the substance to be examined, of length z^ with 



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] 12 Dr. 0. J. Lodge on a Method o/meamrinff the 

flat faces^ and to sqneeze it between two copper or iron rods 
(or any other metal whose condactiyity is well known) of 
exactly the same cross section as itself both in shape and size^ 
pntting a pad of a few thicknesses of tinfoil between the sur- 
faces, so as to make better contact, and then to obserye the 
curve of temperatore down each rod when one end of one is 
heated and the further end of the other is cooled, the whole 
having been left long enough to attain a permanent state. 

Conduction through a cylinder inserted between a pair of metal 

rode. 
3. Let the cylinder be of length Zj 
and conductivity x> 
and let its surface have the radiation-coefficient h\ 
Let the packing on each side be of thickness y, 

and conductiviiy Kj 
and let it be so thin that radiation from its edge is negligible. 




Also let us take the atmospheric temperature as an artificial 
zero ; so that by " temperature " we shall always mean excess 
of temperature above that of the air. 

And let T and © be the temperatures of metal and cylinder 
on each side of first packing (see fig. 1), 
Hf and & ditto on each side of second packing. 
Then the quantity of heat which leaves the first rod traverses 
the first packing and enters the cylinder, which is expressed 
analytically thus (A being the conductivity of the metal), 

,dT_ e~T _ d© 
''dx''''~^^'^dx' • • • • U) 

and similarly for the quantity which crosses the second packing, 

.(TT' T'-©' dW 

four equations from which the unknown quantities, -, ©, and 

©^ can be eliminated, and ^ ^ found. 

Now the curve of temperature down the cylinder is, from 

5 1' 

^=© cosh y*F— (© coth qz^%^ cosech qz) sinh qx^ . (3) 



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Absolute Thermal Conductivity of Crystals ^c. 113 

'''^'^ y'=f , (4) 



hence 
and 



-J- =7 (O' cosech qz^% coth qz) 
-j^ =r q (^ coth qz^% cosech hz). 



Subetitating these yalnes in equations (1) and (2) and elimi- 
nating^ we get from the first and second of each set 

e— +e^— =T— +Ty— =~(TT')- 

dx dx dx dx dx^ ' ^ 

also from the first and third of each set, 

© = — ( -J— cosech yr—^cothy^rj, 

0^= — f -T- coth je— -J— cosech qz\. 
Therefore, combining all these, 

/rfT^y_ /dry 

va • V ^dx' \dx/ ,-. 

^smh^^rr (5) 

Txi^) 

Hence x ^ determined in terms of q, which itself contains it 
together with the radiation-coefiicient h! (which must be sup- 
posed known). We may write the last equation thus, by (4), 



sinh qz ^ sk 



/dry _ /dry 

\dx) \dx) 



q pf-^^T;-^-' • • • • (6) 

dx dx 

which shows that this method is not satisfactory for determi- 
ning a when the product qz is very small. 

4. Now there are three special cases, depending on the value 
of Vi- 

When the crystal has its natural surface, and the value 
is determined by special experiment on its rate of cooling. 
In this case the above equation remains as written, and may 
be treated, as qz wiU generally be less than unity, by expan(t- 
ing the left-hand member. 



of A' is 



:(..f.f....), 



|3 - |5^ 

and ihen solving for q by sacoessive approximations. 
Phil. Mag. S. 5. Vol. 6. No. 29. Feb. 1878. 



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114 Dr. 0. J. Lodge an a MetJwd ofmeaxuring the 

(2) When the crystal and rods are covered over with a coat 
of varnish (as Branswick black), so that h is the same for all. 
In this case the coefficient of the right-hand member becomes 

simply ~j, bnt the treatment required is the same as in the first 

case. 

(3) When the crystal is surrounded with cotton-wool or felt, 
or in some other way has its exterior surface made adiabatic, 
so that 7/ =0. In this case the left-hand member of the above 
equation equals z^ and the right-hand becomes indeterminate, 
so that a fresh investigation is necessarj\ 

Ccae when radiabum from the exterior surface of the cylinder 
is prevented. 

5. Heat will now flow through the cylinder as through part 

of an infinite wall, and ^ becomes simply ; hence the 

two sets of equations (1) and (2) are now all equal to one 
another, and they reduce to 

dx J/ ^ z y ^ ^ 

But as these are only three equations between four unknown 
quantities, some further observation is necessary before we can 
determine v. We may either omit the crystal altogether, or, 
what is probably better, replace it by a piece of the same metal 
as the rods are made of, and repeat the temperature-determi- 
nations, the packing being kept exactly the same as before. 
Denoting the temperatures in this case by small letters, the 
equations will now be 

,dt /0^t\ ,^-5 {^-^\ ,o^ 

where z^ is the thickness of the bit of metal. By these three 
equations - is determined ; and its value may then be substi- 
tuted in the former set. 

Eliminating 8 and 0' from the former set (7), we have 

(^¥)S-^-^ (») 

similarly from (8) we get 



(t -¥)§=<'-'. 



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Absolute Thermal CondttetivUi/ of Crystals ^c. 116 



(10) 



whence, getting rid of- , we have 

k _ , T^-T e-t 

da dx 

80 % is determined by the two observations. 

6. Although this method requires two experiments while 
the other (§ 3) required only one, yet it will probably be more 
useftil than the other, as it is applicable to very thm slices of 
crystals — ^in fact the thinner the better, — ^whereas the other one 
applies more to substances in the form of a short rod ; for it fails 
when z becomes very small. This failure of the § 3 method is 
due to the fact that it depends entirely on radiation going on 
from the cylinder at the same intrinsic rate as from the rods, 
and on some appreciable quantitv of heat being lost in this 
way during its passage through the cylinder ; hence of course 
a certain length of the cylinder is essential. 

Observation of the Curves of Temperature, 

7. We have seen (§ 1) that, to determine the curves of tem- 
perature, it is necessary to know the actual temperature of two, 
or perhaps one should rather say three, points on each rod. 
Each rod then should have three holes bored to receive the 
bulb of a thermometer, one near eaqh end, at a distance I from 
one another, and another in the middle halfway between the 
other two. Let the temperatures which these thermometers 
indicate above that of the air at the time be denoted by T^,, T^, 
Ti, Tj, Tj, T3, their position being shown in the figure. 

Fig. 2. 




It€ or 

m^BMgMUttf, 
Denote the distances thus : — 

Oa=Zo=i3, 
la=/i=6 2, 

01 = Z=23=/o-ii; 
then measuring x from for the first rod, we have as the curve 



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116 On the Absolute Thermal Conductivity of Crt/stale, 

of temperatare down it^ by § 1^ 

^ = A cosh^^— B sinh^^ ; 
that is, 

t=ToC08h/)j?— (T^coih^Z— TiCosech^Qsinh^^ ; . (11) 

similarly down the second rod, reckoning a from b, the curve is 
^ = A' cosh 2?^ — B' sinh^^^ 



where 



and 



A/_ % sinh j??Q— Ts sinhp?i 
"" sinhpZ 

•p/^ Tg coshyZp— Ta cosh jpZi 
"" sinhj^Z 



(12) 



Thus 



We can now at once express the values of the " known quanti- 
ties '' which occur in equations (1) and (2), and in the right- 
hand members of equations (5) and (6); viz. 

^. ^- s. "^ s- 

j__ Ti sinhjpZo—To sinhpZi 
sinhjoZ 

= ( ^) = t> TiCoshpZo-T,coshM 
\dx/ x^i sinhj^Z 

rjy_^,_ Tgsinh j>Zo— Tg 8inh;>Zt 
sinhj^Z 

— « l^\ = ~«B^=« Tg cosh pZi-T, cosh pZ^ 
d^ \da/m^9 ^ ^ sinhpZ 

The symmetiy of these expressions is visible in the following, 
where for shortness sh^ is written instead of sinhpZ^, chi for 
coshpZi, and so on : — 



dT 
da 



(13) 



dT 

' pda ' 



m . ^*x^ . _ I sho shi 
I -"-o •'■1 



cho ch^ 
To Ta 



sh^ shi 
ch^ chi 



(14) 



8. We can now write down the value of the right-hand 
member of equation (5) thus^ 

/dT;Y_/dT\» 

\dJ_U^) , p^{(Tsch,-T>ch,)'-(T,ch,-TochO«f ,,,^, 

^dr dT p(TiT,-^T,T,)sinhpl '^^^^ 

<ix da: 



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Application of the Kinetic Theory of Gases to Gravitation. 117 

80 (6) becomes 

sinhgz 

q "" [-(Ti-T,) co&hpk] 

* \ (Tp+Ta) co8hpf^-(Ti +T») ooshK ^ {{T^-T^z)^'^ph .... 
V' (ToT,-TiT8)8iiih/Z '^ ^ 

wliich is a form convenient for calculation. 

9. So also for the second method (^ b\ we can write down 
the value of the quantities occurring m tne right hand of (10), 
T^-T ^ (Ti-T,) 8inhH-(To-T8) sinh^Z^ . 
"dT" j9(To cosh j9^-Ti cosh jt>/o) ' ^ ^ 

dx 

and similarly for the small <'s, of which a set t^^ t^^ t^y t^ have 
been observed. In this case tihere is no loss of heat in passing 
through the crystal ; so we ought to have 

dT^dr; 

dx dx 
which gives the condition 

Ti+T, _ coBhj>fi . 

T„+T,-co8hH' ^^^ 

and unless this condition is satisfied there is some error in the 
experiment^ and it is useless to proceed. 

I have to express my thanks to my brother, Mr. Alfred 
Lodge, of St. John's College, Oxford, for several suggestions 
in the writing out of the above and for some improvements in 
the notation. 

In the second part of this communication some practical 
details will be given, together with the results of some trials 
of the method now going to be made. 

Umversitj College, London. 

XVII. Application of tlie Kinetic Theory of Gases to Gravitor- 
tion. By S. Tolver Preston*. 

No. IILt 

1. TN the last Number of the Philosophical Magazine is a 

J- short paper bv Mr. James CroU on Le Sage's Theory 

of Gravitation, m which he alludes to a difficulty that has 

• Communicated by the Author. 

t For two preceding parts, see Philosophical Magazine, September and 
November 1877 (under title '* On some DTnamical Conditions applicable 
to Le Sage's Theory of Gravitation *'). 



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118 Mr. S. T. Preston on the Application of the 

presented itself to him after reading my two former papers on 
this subject. As any theory that makes a pretention to truth 
onght to court every criticism^ I am glad to notice here the 
difficulty alluded to, at the same time availing myself of the 
opportunity to touch upon certain other points that would ap* 
pear to want a little further elucidation. 

2. The point in question is^ that, since gravity is proportional 
to mass, it is admittedly necessary to assume mat the total vo- 
lume of free space in a substance must be great compared with 
the total volume of matter contained in the molecules of the sub- 
stance (in order that the medium producing gravity may be able 
to penetrate the substance and act upon the molecules in the in- 
terior). Mr. Croll finds a difficulty m reconciling this assump- 
tion with some deductions regarding molecules by Sir William 
Thomson, in a paper published in * Nature.' vol. i. (p. 551). 
Now I think it may be shown clearly here (and that this will 
also be apparent to Mr. Croll on referring more minutely to 
the wording of the above paper) that this paper was not in- 
tended strictly to give molecular dimensionSy but rather mole- 
cular distances (from centre to centre), or number of molecules 
in unit of volume. It is true that an estimate of molecular 
dimensions is given on the special assumption that the radius 
of a gaseous molecule is equal to " half the average shortest 
distance reached in a vast number of collisions." Whether 
this is the actual radius, therefore, depends evidently on 
whether the two molecules come into contact at collision or not. 
This might not be ; and if not, the radius might be smaller. 
Thus it is at least conceivable that a layer of a medium may 
exist between two vibrating approximated molecules, much as 
a drop of water floats on a film of air. I do not wish to insist 
upon this comparison ; but no one will, I think, consider that 
it is necessary that molecules should come into contact ; and if 
not, it is impossible to measure their dimensions, but only 
their sphere of activity. This, therefore, would remove the 
difficulty ; but I do not wish to hold necessarily to this expla- 
nation, as it appears to me that there are some grounds for 
supposing that molecules do come into contact. 

3. The explanation I have to brine; forward is of another 
character. The interstices are in the molecules themselves. 
This explanation was also, I believe, suggested by Le Sage 
himself. The old notion of a molecule bemg a hard spherical 
mass certainly appears rather crude. In view of the numbers 
of difierent capacities for vibration possessed by a molecule, 
as proved by the spectroscope, it appears a necessary deduc- 
tion that a molecule must be of a complex structure. Inter- 
stices would make it complex. In ordinary architecture we 



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Kinetic Theory of Gases to Gramtatioru 119 

do not observe a solid block structure^ if I may so express it, 
but a more or less open structure as consistent with lightness 
oranbined with elasticity. So molecular architecture (as size 
is only relative^ and principles apply everywhere the same) 
may be of an open structure, as consistent with elasticity. 
This open structure, inyolving various separated parts, would 
give the molecule the faculty of taking up various vibrations, 
as it is known to be capable of doing. 

4. Admitting, therefore, molecules to possess an open struc- 
ture, the passage of the gravific medium through the mole- 
cules of matter might be compared (merely for a simile) to 
the passage of a stream of air through a scaffolding, the air 
passmg in great part through, but exercising a gentle pressure 
against &e solid parts of the scaffolding. So, in analogy, with 
the gravific medium ; or by this open structure of molecules 
we have all the conditions for the pressure termed ^^ gravity,*' 
together with the permeability essential to make gravity pro- 
portional to mass, [^e make no postulate as to tiieform of 
open structure.] 

5. One point may be noticed here in connexion with the 
inference tnat the molecules of solids are in contact. The old 
postulate of perfectly riffid molecules put a difficulty in the 
way of assuming that the molecules of a solid are in contact, 
becnuse the "elasticity" (or compressibility within certain 
limits) of a solid could scarcely be reconciled with this postulate 
of perfectiy rigid molecules. The dj-namical theory of molecules 
put forward by Sir William Thomson, which explains the elas- 
ticity of a molecule by a simple motion of the matter forming 
it, enables us to explain the elasticity of a solid (with mole- 
cules in actual contact) In/ the elasticity/ of the molecules them" 
selves. By this theory also the open structure we have sug- 
gested becomes a natural consequence. 

6. That matter does possess an open structure, due to some 
cause, appears to be sufiiciently proved by independent facts. 
How otherwise could waves of lignt and the magnetic disturb- 
ance pass so freely through matter? It appears natural to 
assume that the molecules of a solid are in contact, on account 
of the resistance they oppose to displacement in all directions. 
If so, it would appear necessary to look for the interstices in 
the molecules themselves ; and we think we have shown that 
this conclusion is not merely warranted by the case of gravity, 
but that it is in itself rather probable on independent grounds. 

7. It mav be observed that, by means of interstices in the 
molecules themselves, a mass may possess any degree of open- 
ness and yet be practically closed — i. e. closed to the penetra* 
tion of all ordinary matter, such as the air, liquids, Ac, — as 



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120 Mr. S. T. Preston on the Application of the 

evidently one molecule cannot readily penetrate into the inter- 
stices of another. On the other hand^ the minute particles of 
the gravific medium pass through them with perfect freedom ; 
and though these interstices are so small^ they are on tiie other 
hand so numerous (on account of the number of the molecules) 
that their total sum may represent a relatively very large va- 
cant space. Under these conditions matter may be practically 
solid or continuous, because impenetrable by the finest por- 
tions (molecules)' of other matter^ and yet possess any desired 
degree of openness. 

8. We would add a few remarks here in regard to the logical 
necessity of seeking a cause for gravitation. To do so is, 
as it seems to us, simply to look for an explanation of a natural 
phenomenon consistent with reason. One sometimes comes 
across the remark that the efiPect is an ultimaie one, incapable 
of explanation. But then the physical investigator does not 
readily surrender the right of using his reason ; or we really 
have no power to assume that physical effects are brought 
about in a way incapable of appreciation by the reason, flie 
most eminent minds have admittedly been in favour of an ex- 
planation. This was so (as is known) with Newton and 
Faraday. Count Bumford says, " Nobody surely in his sober 
senses has ever pretended to understand the mechanism of 
gravitation." Physical effects are generally admitted to be 
fundamentally efiects of motion (however aiverse they may 
be). The one fundamental cause, therefore, to get an insight 
into in physical science, is the cause of the development of 
motion. If we made an exception to this in any case (or 
assumed the motion developed was an ultimate fact incapable 
of explanation), then this would be pursuing a course wnich, 
if carried out in its entirety would leave nothing to be explained 
at all ; for it should be observed that the development of mo- 
tion is in principle the one physical efiect that requires expla- 
nation (from the fact that all physical effects are efiects of 
motion). This inference surely deserves a mature realization. In 
the case of gravity we observe a motion of approach developed 
in two masses. Here, therefore, we have an instance of the 
one fundamental fact for which in principle an explanation is 
required. We require an insight into the cause of the deve- 
lopment of this motion in the two masses. We want something 
more than merely to obseiTe the fact of the motion ; we want 
(among other things) to understand why the energy of the 
motion developed has the particular intensity observed — also 
to account for the remarkable fact that the intensity diminishes 
in the complex ratio of the square of the distance, and not in 
some other ratio. Surely if any thing requires an explanation, 



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Kinetic Theory of Gases to OravitcUion. 121 

we have someihiDg to explain here. What^ for example, 
would be thought of any one saying that the intensity of light 
varied as the square of the distance because it was its ^^ pro- 
perty " to do so. The worst of this want of appreciation of 
the logical necessity for an explanation is,' that the attention 
is called away and the inquiring faculties deadened, and thus 
these grand problems secure a share of attention which is 
utterly insignificant compared with that devoted to those of 
minor importance. 

9. To prevent any misconception, we would remark here 
that the uieory we have to suggest as an explanation of gravity 
is different in several essential points from that of Le Sage. 
The theoiy of Le Sage was dynamically defective in several 
essential points (probably owing to the comparatively small 
advance made in dynamics at his time). His assumption of 
continuous streams of particles coming from a number of dif- 
ferent directions equiangularly scattered in space, the particles 
being sapposed to come from indefinite distances (^^ ultramun- 
dane " particles), must appear evidently somewhat fantastic ; 
for it appears inconceivable how the motion of such a system 
of streams of particles coming from ultramundane space 
should be kept up without confusion ensuing, owing to the 
mutual collisions of the particles of the streams which cross 
each other in all directions, if ^as he assumed) each separate 
stream were to move continuously in one direction. For, how- 
ever much the collisions might be reduced by reducing the 
size of the particles, they must occur in a long course of time, 
especially considering the high velocity at which it is neces- 
sary to assume the streams to move. Moreover the great ob- 
jection to this view is that it involves, for the maintenance of 
gravity in the visible universe, a continual supply of matter 
from ultramundane space. This objection Le Sage distinctly 
recognized and could not surmount. The real merit of his 
theory was his fundamental idea that " gravity,*' or the ten- 
dency to approach of two masses, was due to the one mass 
sheltering or screening the other from the action of the streams 
of particles in which the two masses of matter were immersed — 
so that the remote sides of the two masses (where there is no 
shelter) are struck by a greater number of particles than the 
near sides (where there is shelter), and thus the two masses are 
urged together. The rest of his assumptions are in the nature 
of postulates, some of them unrealizable. He had little know- 
ledge to draw upon at his time. 

10. The points we have to bring forward are briefly as fol- 
lows. We do not assume, as Le Sage did, the existence of 
streams of particles flowing as continuous currents in assigned 



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122 Mr. S. T. Preston on the AppUeation of the 

directionB and coming from indefinite distances (or ''ultra- 
mnndane " particles, as he termed them). We do not assume 
that the particles producing gravity in the visible universe 
converge towards it in streams from ultramundane space. Oo 
the contrary, we assume that the matter producing gravity 
within the confines of the visible universe is a« a lohole at 
rest ; or we regard the medium producing gravity simply as 
a gas. This gas difiers from an ordinary gas only in the mul- 
tiplicity of its particles, their excessive minuteness, and (con- 
sequently) extremely long free path. It is a direct consequence 
of the kmetic iheoiy of gases that, within the range of free 
path of the particles of this gas, the particles move in precisely 
the right way to produce gravity ; t. e. all the assumptions that 
Le Sage maae arbitrarily as regaids the motion of his streams, 
take pkce as inevitable necessities unthin the range of free path 
of the particles of a gas. The motion of the particles (in such 
a way as to produce gravity) is automatically kept up by a 
process of self-adjustment ; i. e. gravity is the inevitable result 
of the existence of a medium in epa>ce constituted according 
to the kinetic theory of gases. It has been mathematically 
proved that the particles of a gas, within the range of free path, 
move uniformly or equally towards all directions. This special 
character of motion is automatically kept up under the influ- 
ence of the collisions ; or, however each particle (by itself) 
may change its course, ihis general cJiaracter of motion is 
rigidly kept up, and is required to satisfy the condition of 
eqiud pressure in all directions. But this motion of particles 
uniformly or equally in all directions is precisely what is re- 
quired for gravity. 

11. The only mrther condition necessary is, that the range 
of free path of the particles should be great enough, so that 
(approximately) uninterrupted streams of particles move 
through the mil range through which gravity has been ob- 
served to act. This length of free path (by any given number 
of particles in unit of volume) may be increased to any extent, 
simply by reducing the size of the particles. Taking, there- 
fore, the visible universe as a whole, we have no streams of 
particles, but simply a gas at rest. The streams only exist 
within the range of free path of the particles, or within the 
range of gravity. We may compare the medium filling the 
visible universe to the air of a room, in which there are no 
streams, but the air is eu a whole at rest. Contract the room 
(in imagination) up to the range of free path of the molecules 
of air, and we have streams of molecules sweeping in all direc- 
tions through the room. The space in which we observe 
gravity may be compared to this contracted room, within 



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Kinetic Theory of Gases to Oravitation. 123 

which streams of particles are sweeping through aniformly in 
all directions, the uniform motion of the particles equally in all 
directions (necessary to produce gravity) being automatically 
kept up under the influence of the mutual collisions^ in a way 
demonstrated to take place in the case of a gas. It should l>e 
observed that this self-adjustment of their motion by the par- 
ticles is not a mere result of chance, but a rigid adjustment of 
such a character that, if the uniformity of the motion were 
artificially disturbed, the particles when left to themselves 
would immediately correct the irregularity. The above length 
of free path, though great in one sense, becomes small and 
suitable for a gas pervading the vast range of the visible 
universe. Unl3:e Le Sage, we do not object to the collisions 
of the particles among themselves ; for these collisions (in the 
case of a medium constituted as a gas) maintain the uni- 
formity of motion. We require no supph/ of matter to produce 
gravity, and no supply of energy. The Energy is self-con- 
tained. It is simply the case of the normal motion of the 
particles of a gas. Motion is as natural as rest. Nothing 
surely could be more simple than these conditions. 

12. It might be said that this theory implies a limited range 
to gravity. It may be extended to any desired range simply 
by making the particles small, and consequently the free patn 
great. We venture to think that rather than that a theory 
should be required to explain that the stars gravitate, a theory 
should be required to explain that they do not* gravitate. 
For surely the idea of an indefinitely extended universe all of 
whose parts gravitated towards each other, would represent 
dynamical conditions of trvstability on the most gigantic scale. 
Imagine the incongruity of the idea of the i^ole universe 
tending to agglomerate in one (perhaps infinite) mass. To 
our mind no ttieory of gravity would be satisfactory that did 
not explain away this. The kinetic theory gets over this 
difficulty in a most complete manner, by allowing gravity to 
take place within a conformable range, without extending it 
to indefinite distances and thereby involving conditions of 
instability. 

13. As we have said, we do not shirk in the slightest degree 
any criticism as regards this theory, but shall be glad to meet 
it, knowing that, if true, it will stand a full examination ; and if 
faJse, the sooner it is proved so the better. There is one other 
point on which perhaps an objection might be raised. It 
might be said. If a gas exists in space, how is it that we 
do not detect its presence in experiments on the specific heat 
of other gases, this gas being at the same time present ? or 

* Of course we do not refer to double stars, in close range. 



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124 Mr. S. T. Preston on the Application of the 

why does not some of the heat pass from the gas experimented 
on to this gas ? In answer to this, it must be kept in view 
that the gravific medium, though in principle constituted as 
an ordinaiy gas, differs from an ordinary gas profoundly in 
several respects. First, it is necessary to assume that its 
particles are (as essential to the long free path) incomparably 
more minute than those of an ordinary gas, and the number 
of particles in unit of volume much greater. A molecule of 
an ordinary gas surrounded by the particles of the gravific 
medium, might be compared (as regards relative dimensions) 
to a visible mass surrounded by the molecules of air. Next, 
it is necessary to assume that the velocity of the minute par- 
ticles of the gravific medium is incomparably greater than that 
of the relatively massive molecules of ordinary gases. Now, 
it is a known fact that the resistance to the passage of bodies 
through a medium constituted according to the kinetic theory 
diminishes as the normal velocitjir of the particles of the medium 
increases. By making, therefore, the normal velocity of the 
particles of the medium sufficiently great, all perceptible re- 
sistance to the passage of bodies through it will disappear. 
It is as if the medium did not exist; it becomes quite impalpable, 
or its presence impossible to detect. This is consistent with 
observation. The amount of energy, or motion, abstracted 
from a body passing through the medium, and given up to 
the medium, is exactly measured by the resistance encountered 
by the body. It is this transference of energy to the medium 
that constitutes the " resistance." If, therefore, there is no 
measurable resistance te the passage of the body through the 
medium, there is no measurable energy abstracted from the 
body. This gets over our difficulty ; for since the molecules 
of ordinary gases (at their relatively slow velocity) move 
through the gravific medium without appreciable resistance, 
there is no perceptible transference of energy (i. e. " heat ") 
from them to the gravific medium. In other words, the 
presence of the gravific medium cannot interfere with the ex- 
periments on the specific heat of ordinary gases. In short, 
the high normal velocity of the particles of the medium 
necessarily renders it in all respects completely impalpable, or 
its presence impossible to detect by the senses. The high 
velocity of the particles is only naturally adapted to me 
minute size of the particles. 

14. It would seem difficult to avoid the application of the 
above principles to the case of molecules in dose proximity — 
"cohesion" or "chemical union." For, first, it would ap- 
pear obvious that molecules in contact would be urged together 
with eaceptianal force, owing to the parts in contact cutting 



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i( 



Kinetic Theory of Gates to Gravitation, 125 

off the entire stream of particles*. Secondly, the shapes of 
diverse molecules (which would have no particular influence 
while the molecules were at a distance) would, when the mo- 
lecules are in contact, have a great influence, according to 
whether the solid parts (or interstices) fitted over each ower, 
so as to afford more or less shelter from the streams of particles. 
Possibly this might account for (or at least throw some light 
upon) the extraordinary varied oehaviour of chemical ^^afi- 
nitt/.*^ If this were justified, it would certainly be a remarkably 
simple cause. It is just possible that a thing may be missed 
sometimes by looking too deep. The processes of nature are 
as a rule recognized to be simple, this being the necessarv 
condition for order, " Simplicity is the soul of mechanics.^* 
This view, if well founded, would have the advantage of cor- 
relating cdl molecular actions (including '^ gravity '') under 
4me cause. We have thought it just as well to mention these 
views in passing (without attaching the same definiteness to 
them as we attach to gravitation). 

15. We would in conclusion make a few remarks upon a 
matter of principle connected with this subject. It must be 
evident that under a dynamical theory of gravitation, when a 
mass is Hfted, the energy expended in liftmg cannot be con- 
verted into ^^ potential energy, but must be converted into 
kinetic energy, in imparting motion to the particles impinging 
upon the upper side of the mass, and which tend to urge it 
downwards. Conversely, when the mass falls, kinetic energy 
is transferred from the particles of the medium to the mass. 
As a general principle, therefore, by the abandonment of the 
theory of ^' action at a distance,^^ tnere can be no such entity 
as ^^ potential " energy at all. We cannot avoid thinking that 
the very neoessiiy to put forward a theory, that energy can 
possess, as it were, a double nature (kinetic, and not kinetic), 
m order to harmonize with the theory of " action at a distance,' 
is by itself a sufficient logical condemnation of this latter 
theory. The idea of ^^potenticd^^ energy (t. e. an energy 
which is not kinetic) involves the inconceivable idea of an 
energy withotU motion, L e. a kind of spiritual energy, whose 
existence or non-existence leaves matter in the same physical 
state. Already serious doubts have been cast upon its validity 
as a logical principle by some of the most eminent minds. 
From me prevalent use of the term ^^ potential " energy, and 
at the same time the common repudiation of the theory of 
^^ action at a distance," one would be inclined to draw the in- 
ference that there was an idea to a certain extent prevalent 

* We believe Le Sage called attention to this in its application to 
''cohesionr 



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126 Application of the Kinetic Theory o/Oaeee to GravitcUion. 

ihatthis term ^^ potential " energy oonld still be used in a certain 
sense^ even after the theory or action at a distance had been 
abandoned. We think it can be clearly shown that this is not 
le^timate. For, by the rejection of the theory of " action at 
a distance/' external matter or a medium (in a state of motion) 
mnst be concerned in developing motion in matter; and 
therefore it most be a case of kinetic energy, not ^^ potential " 
energy. Either (for example^ the motion of approach of two 
masses (or molecules) is deyeloped ^as supposea) tvithout the 
concurrence of external matter, or (secondly) this motion is 
simply transferred to the masses from external matter. In 
this latter case (which represents the case where the theoiy of 
" action at a distance " is rejected) the energy exchanged can 
only be the energy of motion (kinetic energy), not, therefore, 
^^ potential " energy. It might, perhaps, be urged that even 
when the theory of" action at a distance " is rejected, a raised 
mass can still be said to have ^^ potential " energy (due to its 
position), because it can fall. This, however, may be proved 
not to be legitimate. For, from the very fact that (by the re- 
jection of " action at a distance ") the energy expended in 
raising the mass was converted into kinetic energy, it cannot 
have been converted into ^^ potential " energy (i. e, an energy 
which is not kinetic) as well, A doitble equivalent of energy 
cannot be generated*. We think we have clearly shown, 
therefore, that by the rejection of the theory of " action at a 
distance," the idea of ^^ potential " energy must (to be lo^cally 
consistent^ be unreservedly abandoned. The rejection of 
^^ potential ^^ energy makes all energy of one chanicter, viz. 
energy of motion ; and then the great principle of the indestruo' 
tibUitt/ of motion inevitably presents itself for acceptance. 
With the theory of '^ action at a distance," the idea of ^^ force " (in 
the old sense of an action across space without the intervention 
of matter) must be given up. Thus we have in the physical 
world, only the two great frindamental conceptions of mcUter 
and motion left ; or all physical phenomena come thus to be 
correlated in one grand and fundamental aspect, viz. as con- 
sisting in the various exchanges and phases of motion, 
London, Jan. 11, 1878. 

Note. — ^We think it right to add that we make no claim to have 
shown (as this had been already done by others) that the molecules 

* To say that a raised weight tending to approach the earth by the 
action of tiie gravific medium, pofisessed *^potentidl " eneigy becauae it 
can approach tne earth, would oe like saving that a ship confined by a 
cable and tending to approach a rock by the action of the wind, possessed 
^potential " energy, because it can approach.the rock (by the breakmg of 
the cable). The cases are evidently parallel. 



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Electromagnetic and Cahmetric Absolute Measurements. 127 

of a gas regulate their motions so as to move in a particular manner, 
though we doubt whether, if we had not arrived at this conclusion 
independently for ourselTes, we should have been able to make a 
practical application of it. The point it has been our object to call 
attention to (and which apparently has not been noticed by others) 
is, that the motion of the particles of a gas within the range of free 
path precisely satisfies all the conditions Le Sage arbitrarily assumed 
in order to produce gravity — or that the special character of the 
motion Le Sage arbitrarily assumed his streams of particles to have, 
actoally eoeists within the range of free path of the particles of a gas 
— ^in other words, that all the effects of gravity can be produced by 
ihe mere existence of a gas in space^ and indeed must be produced if 
such a gas exists. 



XVIII. Electromagnetic and Calometric Absolute Measwremen ts: 
the Absolute Value of Siemens' s Unit of Resistance in Electro- 
magnetic Measure ; the Relation between the CurrenJt-work 
and the Heat-evolution in stationary Galvanic Currents ; and 
the Absolute Values of some constant Hydroelectromotive 
Forces in Electromagnetic Measure. ( Condensed Comparison 
of the Results of a Series of Investigations.) By H. F. 
Weber, Professor of Mathematical and Technical Physics 
at the Federal Polytechnic Academy of Zurich. 

[Continaed from p. 48.] 

m. Tlie Heat produced by Stationary Galvanic Currents. 

MR. JOULE, thirty-seven years since, showed by experi- 
ment that the quantity of heat which a stationary gal- 
yanic current of intensity i generates in a conductor whose 
resistance is w, during the time z^ is proportional to ^wz. Sir 
W. Thomson dien, in 1851 (and Prof. Clausius and others 
later), proved in the theoretical way that the value of the me- 
chanical work which is expended in the stationary galvanic 
current of the intensity t, in a conductor with the resistance w, 
along which the electromotive force E is in action, in the time 
z is equal to the product lEz, or, pursuant to Ohm's law, equal 
to the expression Pwzy where the quantities E, t, w are to be 
taken as measured according to absolute measure. If we 
make the assumption that, in a stationary galvanic current in 
which the evolution of heat is the only action of the current- 
flow, the amount of heat developed in the unit of time, Q, is 
the full equivalent of the work expended in the same time, 
then we nave 

JG=i'M7=tE, 

where J denotes the mechanical equivalent of the unit of heat. 

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128 Prof. H. F. Weber on EUctromagnetie and 

On this hypoihesis^ consequently, the proportionality-factor of 
Joule's law of heat-evolution is equal to the reciprocal yalue 
of J. Supposing that this assumption, the whole of the me- 
chanical work consumed by the stationary galvanic current 
appears in the form of heat, is correct, we have a n£w definition 
for the absolute resistance of a conductor : — ^The absolute re- 
sistance (measured according to any system) of a conductor 
is equal to the mechanical value of me amount of heat which 
is generated in the conductor in the unit of time by the con- 
stant galvanic current 1 (measured according to the same 
system of measurement). And a new method for the experi- 
mental determination of the absolute resistance of a conductor: — 
Measure the amount of heat, Q, which in the time z is gene- 
rated by the constant current i measured in absolute measure ; 
then the absolute value of the resistance (measured in the 
same system of measurement in which i is measured) is 

It cann(tt be maintained that the cori-ectness of the hypo- 
tJiesis, " in the stationary galvanic current the entire work of 
the current is converted into heat," is so far above all doubt 
that one can without hesitation make use of the heat developed 
in a conductor by the stationary galvanic current for the abso- 
lute measurement of' the resistance of the conductor. The 
results of the most exact investigations which have yet been 
instituted in this direction for testing the fundamenM hypo- 
thesis in question contradict one another. Von Quintus 
Icilius (Pogff. Ann. vol. ci. 1856), in a carefully executed 
very extended series of operations, obtained the final result 
that the stationary galvanic current develops about 7 per 
cent, more heat than it should according to Thomson's equa- 
tion ; on the other hand. Joule *, in a comprehensive and very 
accurately executed investigation, with which he was charged 
by the British-Association Committee for the production of 
standards of resistance, found by experiment that in fact almost 
as much heat is produced in a conductor by the stationary 
galvanic current as is specified by the above-mentioned law. 
Yon Quintus Icilius calculates from his experiments the 
mechanical equivalent of the unit of heat to be 399*7 metre- 
kilograms ; Joule infers from his the value 429*3 metre-kilo- 
grams for J (expressed in the tisual measure of mechanical 
work). While the discrepancy between the results of these 
two series of observations is not cleared up the galvanic heat- 

• Reports of Electrical Standards, edited by Jenkin, p. 165. 

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Calametric Absolute Measurements. 129 

development cannot be nnhesitatinglj made use of for the 
absolute determination of resistance. 

In order to procure the means to enable me to carry out an 
entirely unexceptionable determination of the absolute value 
of the S. M. U. by the heat-evolution of stationary galvanic 
currents, I undertook, in a very extensive and in many ways 
varied third experimental investigation, as rigorously exact a 
solution as possible of the question : — In a stationary galvanic 
current in which evolution of heat appears as the only action, 
is the heat generated in a certain time the eacust equivalent of 
the mechanical work consumed by the current during that 
time? 

In the path of a current maintained constant, of which the 
absolute intensity t was carefully measured electroma^etically, 
was placed a thin platinom wire of about 15 S. M. u . resist- 
ance, wound in zigzag upon a numerously perforated frame 
of hardgum. Thick copper wires conducted the current to 
and from the platinum wire. The frame carrying the Ttdre 
was suspended in a water calorimeter of the thinnest sheet 
copper, which was in an environment of constant temperature. 
The water filling the calorimeter amounted to about 250 grams ; 
the water-worth of the calorimeter-vessel, the frame, and the 
ttiermometer amounted to about 3 ^rams. 

The constant current with the intensity t was conducted, 
during the time z, through the resistance w in the calorimeter. 
The mechanical work consumed by the current during this 
time, within the conductor with the resistance to, was then 
fwz. On the other hand, a certain amount of heat Q was 
generated in the resistance w, was given up to the calorimeter, 
and was to be calculated from the rises of temperature in the 
calorimeter, the water-worths of the substances filling the 
calorimeter, and the losses of heat of the calorimeter by radia- 
tion outwards or the gain of heat by the calorimeter from 
without. The mechanical value of this amount of heat, JQ, 
would necessarily, if the total work of the current were con- 
verted into heat, be equal to ^wz. 

On the hypotheses that the entire work of the current is 
converted into heat, that the exchange of heat between the 
calorimeter and its surrounding is governed by Newton's law, 
iliat the specific heat of water increases linearly with the tem- 
perature, and that the resistance of the platinum wire used in- 
creases proportionally with the temperature, the following 
difierential equation nolds for the dependence of the variable 
temperature t of the calorimeter on the time z: — 

PhU. Moff. S. 5. Vol. 5. No. 29. Feb. 1878. K 

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130 Prof, H. F. Weber on Electromagnetic and 

In this equation, M denotes the sum of the water-worthfi of the 
sabstances filling the calorimeter^ ^« the constant temperature 
of the environment of the calorimeter ; <;« the specific heat of 
water, and to. the absolute resistance of the platinum wire, at 
the temperature t^ ; 7 the coefficient of the increase of the 
specific heat of water, and q the coefficient of the increase of 
me absolute resistance of the platinum wire, for 1° rise of tem- 
perature ; and h the heat which the calorimeter would part 
with to the outside if its temperature were 1^ higher than that 
of its environment. 

If we put X= Tur* and B= VKr — - and assume 

that at the time z^O the temperature of the calorimeter is 
equal to to, the integration of the above difierential equation 
gives the following connexion between the variable temperature 
t of the calorimeter and the time z : — 

or if the notion ^^ mean temperature of the calorimeter during 
the time z^O to zs^^z " be introduced with the symbol ?, 

JMc,[«-^o+B(?-<.>=i«u7^ (2) 

The quantity B(?— ^«)xr represents the temperature-correction 
which must be applied to the direct reading of the rise of tem- 
perature of the calorimeter on account of the heat-exchange 
with the environment, and on account of the variability of me. 
resistance as well as that of the specific heat of water with 
rising temperature. This correction can be made as small as 
we please, by a suitable selection of the quantity i~^t^. In 
all tne measurements executed, care was taken so that this 
difference only amounted to so small a fraction of a degree 
» that the correction, 'B{t'-ta)z, to be added to f — «© amounted to 
} only from g^jy to ^^ of t—t(^ The period z was chosen so 
J great that the rise of temperature amounted to about 15°. For 
the determination of the mean temperature t of the calori- 
meter, and of the constant B, the temperature of the calori- 
meter was read off, from the commencement onwards, every 
five minutes ; in this way a series of equations of the form (1) 
were obtained, from which B could be ascertained. The ther- 
mometer of the calorimeter was most carefully compared, within 
its entire scale, with the air thermometer ; all readings taken 
from it were always reduced to the indications of the latter 
instrument. 



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Caiometric Absolute Measurements. 131 

The curreni»mtensit7 t was measured in absolate eleotro- 
magnetic measure bj means of the already mentioned simple 
tangent-compass (Bs=165'7 millims.) according to the relation 

for the measurement of u, mirror, telescope^ and scale were 
made use of. To eliminate the daily variations of H^ which 
on some days may reach ^ per cent, of the mean value, H was 
determined^ for the place of the tangent-compass, be/ore and 
after each measurement. The variations of declination of the 
earth's magnetic force (which towards noon are very consi- 
derable for delicate measurements) were eliminated by regu- 
larly recurring, rapidly executed reversals of the current. A 
very powerful damper enveloped the ma^etic needle of the 
compass, and permitted the readings of the deviations of the 
magnet to be taken again 20 seconds after the reversal of the 
current. The intensity of the current was maintained constant 
within yj^ or ^^ of its value by aid of a Dubois- Reymond's 
rheochord in the path of the current. The quantities / and 

3 P 
were so small that the sum of the two corrections, "" 7 ^ + ^i 

amounted to only +0-0008. 

The absolute value of the resistance w was determined by 
the method described above in section II. As the tempera- 
ture tf^ of the calorimeter-environment varied somewhat from 
one day to another (up to 3^), the coefficient of the increase 
of the resistance for 1^ of rise of temperature had also to be 
known. To obtain the latter the absolute value of the resist- 
ance vj was determined for the two temperatures (maintained 
constant) 0^ and 23^. At the same time the value of w for 
the same temperatures was measured in relative Siemens 
measure. The resistance of the platinum wire was found as 
foUows: — 



Tempera- 


Li absolute measnre. 


Id relatiTe measuie. 


Date. 


2§-5 


14-498 xlO^oC"'^ 
\ sec. 


^) 


15-141 S.U. 


Oct 14, 1876. 


22-9 


14-419x10" 


}} 




16-142 „ 


W I^> 99 


28-7 


14-486 xlO^" 


V 




15154 „ 


99 16, „ 





14-141 X 10" 


}} 




14-782 „ 


J, *■, „ 





14-121 X 10" 


}} 




14-791 „ 


99 1"> >9 





14-130x10" 


99 


•r^ t 


14-770 „ 


W ^^9 )9 



E2 

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132 Prof. H. F. Weber on Electromaynetic and 

For 23° the platinum wire possesses the absolute resistance 

14-468 X 10^0 C^i^), 
\ sec* / 

and the relative resistance 

15-146 S. M. U. ; 
and for 0° the platinum wire possesses the absolute resistance 

14-131 xlO"(^HiiE-), 
\ sec. / 

and the relative resistance 

14-781 S.M.U. 

From the first result it follows that 

1 S. M. U. =0-9552 X 10^« /5?!!1!!5:):; 

\ sec* / 

from the latter, 

1 S. M. U. =0-9560 X 10" (^^iyi??:),— 

\ sec* / 

which are in perfect harmony with the results previously ob- 
tained in sections I. and II* We obtain the coefficient of the 
increase of the resistance, referred to 1° of temperature- 
increase : — 

From the absolute measurements, ^=0*001035**) 
And from the relative measurements, j= 0-001074. J 

For the temperature tay employed in the experiment in ques- 
tion, the absolute value w^ was calculated according to the 
formula 

m;=14-131[1+0-001054<] x 10^«(5™5^). 

\ sec. / 

From the results adduced it follows that absolute determi- 
nations of resistance can be accomplished with such precision 
that the variability of the resistance with varying temperature 
can be ascertained from them very nearly as accurately as 
from resistance-comparisons according to toe bridge-method. 

In the course of the investigation a gradual alteration, of the 
resistance of the platinum by the continual passage of currents 
through it was sought after with peculiar care. On the 16th 
October, 1876, at tne temperature of 23°-7 the resistance waa 
found equal to 15-164 S. M. U., or, reduced to 16°, equal to 
16-032 S. M. U. 

After the wire had served for twelve experiments, in which 
a current of absolute intensity 4 (a round number) passed 
through it during about an hour, it showed, on the 19th De- 



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Calametfie Absolute MeaturemerUs. 133 

oember, 1876^ a resistance of 15*068 S. M. U.. or, reduced to 
the temperature 16^, of 15*035 S. If* U. At the end of twelve 
more experiments, in which a current of about 6 absolute 
miits passed through the wire each time during about 45 mi- 
nutes, the latter showed, on the 28th March, at the tempera- 
ture of le"", the resistance 15*031 S. M. U. 

Acoordinglj, under the influence of continual currents of 
absolute intensitj from 4 to 6 the platinum wire underwent 
no demonstrable alterations. A special investigation showed 
that perceptible permanent alterations in the resistances of 
metallic conductors only make their appearance from a definite 
current-intensihr onwards. 

Without further remarks, the following are the results of 
the investigation. 

Here also I varied the experiments in several wavs. First, 
a series of twelve observations was instituted in which a pro- 
portionallj feeble current passed through the wire in the odo- 
rimeter during a proportionally long period. From these 
twelve observations the following values were obtained for the 
mechanical equivalent of the unit of heat (the numbers are 
based on the ordinary measure of work; and with each is given 
the external temperature t/to which ihe heat-unit on whidi the 
result is based refers): — 

October 20,1876 16-6 42849 

„ 21, „ 16-7 42812 

„ 26, „ 16-3 425-51 

„ 28, „ 181 426-93 

„ 30, „ 18-5 429-93 

„ 31, „ 180 429-56 

November 5, „ 16-2 428-18 

„ 6, „ 16-0 427-28 

„ 9, „ 16-4 426-95 

„ 15, „ 171 428-50 

„ 16, „ 18-0 426-46 

„ 20, „ 19-1 427-19 

Henoe the mean mechanical eqniyalent J of the heat-unit is 
eqoal to 427*76 metre-kilograms (with a probable error of 
±0*28), if the specific heat of wator at the mean temperatare 
employed, ■?,= 17°-2, be pat =1. 

A second series oi twelye measnr^nents was next institated, 
in which a proportionallj stronger corrent was employed 
daring a shorter time. The resolta obtained in this series 
were: — 



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184 Prof. H. F. Weber on EUetnmagnetie and 

Date. ^ • 

Q metre-kilogranis. 

December 21, 1876 19-8 428-36 

„ 22, „ 19-7 430-31 

„ 23, „ 18-7 426-37 

„ 24, „ 18-8 427-50 

„ 25, „ 18-8 427-45 

„ 26, „ 20-0 429-18 

„ 27, „ 20-1 428-02 

„ 28, „ 19-9 429-87 

„ 29, „ 19-4 430-15 

„ 30, „ 19-7 426-93 

„ 81, „ 19-5 427-90 

January 1,1877 19-6 428-96 

AoDording to this the mean mechanical equivalent of the heat- 
miit is equal to 428*42 metre-kilograms (with the probable 
error ±0*26), the specific heat of water at the mean temp»> 
rature <, = 19°-5 employed being put = 1. 

In a third series of experiments the period and the current- 
intensity were chosen such that the rise of temperature in the 
calorimeter amounted, as in the previous experiments, to about 
15°. The proportions, however, were not so closely limited 
as to make the difference t—t^ as small as possible ; rather a 
play of a few degrees was given to it. Toe results of this 
series, in which the exchange of heat between the calorimeter 
and its environment possessed a value four or five times as 
great as in the previous series, were : — 

Date '•- ^- 

. metre-kilograms. 

March 28, 1877 16-1 427-15 

„ 29, „ 16-6 429-80 

„ 30, „ 16-8 429-61 

„ 81, „ 17-8 428-03 

April 1, „ 17-0 426-92 

„ 2, „ 17-7 428-56 

„ 3, „ 18-3 427-91 

„ 4, „ 18-0 429-10 

„ 5, „ 17-7 427-85 

„ 6, „ 18-9 427-52 

„ 7, „ 18-5 428-43 

„ 8, „ 17-9 428-93 

According to this series the mean value of the mechanical 
equivalent of ih» unit of heat is 498*28 metre-kilograms (with 
a probable error of ±018), the specific heat of water, at the 
mean temperature i,=17°-6 employed, being put =1. 



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Calometrtc Absolute Measurements. 135 

Ag the general resnlt of these 36 tolerably accordant expe- 
riments (tne extremes differing at the most only ^ per cent 
from the mean) we get : — The mechanical eanivalent of the 
heat-nnit, derived from the heat-evolation ot the stationary 

Slvanic cnrrent^ has the value 42816 metre-kilograms (with 
e probable error ±0*22), understanding by nnit of heat that 
amount which must be supplied to the unit of mass (1 kilo^ 
gram) of water in order to raise its temperature 1° C. as mea- 
sured by the air thermometer. 

The surest means for deriving, in a purely thermic way, thd 
quantitative value of the mechanical equivalent of the heat- 
unit is unquestionably furnished by the relation between the 
two specific heats of an ideal permanent gas — 

or 

T *-l 

For atmosnheric air the three quantities p^v^, «, and Cp are YeTj 
accurately Known from Regnault's measurements : p^v^^lddl; 
a = 0-00367 ; and Cp = 0-23754. The quantity k has been more 
recently determined for the same gas very carefully by M. 
Bontgen: *= 1-4053. Inserting these numerical values in 
the last equation, and also takinginto account that, according 
to the experiments of Joule and Thomson, atmospheric air ac- 
complishes in alterations of volume, besides the external work 
performed, an internal work equal to about y^ of the external^ 
we obtain from the thermal behaviour of air 428*05 metre- 
kilograms as the mechanical equivalent of the unit of heat. 
The unit on which this number is based is that quantity of heat 
which must be supplied to the mass-unit (1 kilogram) of water 
at 14^ or 15^ in order to bring about a rise of temperature of 
1° (measured by the air thermometer). 

Dr. Joule, in 1849, noted as the most trustworthy result of 
his numerous experiments on friction for the determination of 
the mechanical equivalent of the unit of heat the value 
J =423-79 metre-kilograms. In the calculation of this num- 
ber the specific heat of water was put =1 for the temperature 
14°-4 ; moreover the specific heat of the calorimeter-vessel 
was assumed too high. If tlie necessary correction on account 
of the latter circumstance be added, the result just mentioned 
becomes J =424*39 metre-kilograms. The sixty frictipn- 
experiments made quite recently by Joule have given almost 
exactly the same result, 424-67 metre-kilograms. 

Unfortunately tlie total result of Joule's friction-experiments. 



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136 Prof. H. F. Weber on Eleetramagnetie and 

Jss424*50 m.-k., cannot be compared at once with that ob* 
tained from the behayioor of gaBOS^ J =s 428*95 m.-k. The 
two valaes are referred to quite different nnits : the basis of 
the former is ] ^ of Joale's mercory thermometer ; that of the 
latter is 1^ of the air thermometer. These two nnits maj pos- 
sibly differ 1 per cent. Perhaps^ on reducing his previous 
and his recent friction-experiments to the indications of the air 
thermometer, Dr. Joule .obtains a final result as £ood as iden- 
tical with the value of J that follows frt)m the oehaviour of 



On account of this disturbing circumstance, I hold the value 
J =428*95, drawn from the behaviour of gases, and immedi- 
ately comparable with my above result, to be the most certain 
of those given by purely thermal determinations. Conse- 
quently, from the heat-evolution of stationary galvanic cur- 
rents there comes as good as the same mechanical equivalent 
of the heat-unit as from purely thermal processes*. The hy- 
pothesis that the entire work consumed in the stationary cur- 
rent-flow appears in the form of heat has verified itself. 

There still remains to say a few words on the already men- 
tioned determinations, earned out by Joule and Yon Quintus 
Icilius, of the mechanical equivalent of the heat-unit by gal- 
vanic heat-evolution. 

Dr. Joule carried out 45 experiments, in three series f. 
He regards as the most trustworthy result that of the last 
series, comprising 30 experiments— J = 429*3 m.-k. In the 
calculation of this number the specific heat of water at 18^*4 
was put =1, and it was further assumed that the British unit 

of resistance in fact possesses the asserted value 10^^ I ' ). 

\ sec y 

According to our results this is not quite exactly the case : if 
the ratio of the British unit to Siemens's is as 1 : 0*9536, then 

tiie absolute value of the former is =1-0014 x 10^^ /EllllE^y 

\ sec. /' 

* The two results, Jss428*16 (derived from the ffalvanic evolution of 
heat) and J » 428-96 (determined from the thermal behaviour of the per- 
manent gasefl), refer, as was expressly remarked, to two different units of 
heat : in the former the unit is that quantity which can heat the unit of 
mass of water from 17^*6 to 18^*5 ; in the latter it is that which can heat 
the mass-unit of water from 14° to 15°. Therefore the two results will 
only then be strictly comparable, when the variation of the specific heat of 
water at variable temperature is certainly known. The experiments 
which I have, up to the present, instituted for fixing this hitherto totally 
uncertain quantity are not yet brought to a perfectly satasftctory conclu- 
sion. Yet so much can be positively known, that the reduction of the 
two values of J to the same temperature will bring about only a yery 
sliffht alteration. 

T Reports of Electrical Standards, edited by Jenkin, p. 175. 



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Calometrie Absolute Measurements. 137 

and Joule's result becomes 429*9 m.-k. Unfortunately, in 
ibis measurement also, Joule took for the basis the degree of 
the mercury thermometer, and not that of the air thermometer, 
and thereby made a precise comparison of his final result with 
ours impossible. Thus much may, however, be regarded as 
established, that so soon as Joule s mercury thermometer does 
not differ very considerably from the air thermometer, a tole- 
rably good accordance exists between the results of the mea- 
surements made by Dr. Joule and by myself. 

Yon Quintus Icilius did not gauge the resistances made use of 
in his numerous measurements* according to absolute measure. 
The absolute resistance-values which formed the basis of his 
calculations he ascertained by a comparison of his resistances 
with the second copy of Jacobi's resistance-unit, produced by 
Wilhelm Weber for himself, and gauged by him according 
to its absolute value. This copy of Jacobi's standard was 
=0*9839 of Jacobi's unit; and since, according to W. Weber's 
absolute-resistance measurements, the absolute value of Jacobi's 

resistance-unit is = 0*598 x 10^^ ( '-), the copy had the ab- 

\ sec. / 

solute value 0-5884 X 10*" (5!^^^-). Von Qnintus IcUias 

\ sec. / 

regards as the most trustworthy of his experiments the 34 in 
wmch water was employed as the calometrie liquid. From 
these 34 experiments ne calculates, as the final result, J s 300*7 
m.-k. Sin^larly, this result has not in the least aroused the 
attention of physicists; and yet it was to be inferred there- 
from, either that the measurements which conducted to it were 
very faulty, or that the theoretical views which formed its 
basis needed correction. The essentially different result ob- 
tained by me, in which by repeated trials I could detect no error, 
and the good accordance of which with Joule's results I could 
not but consider a further sign of its approximate correctness, 
caused me to reflect long upon the cause of the discrepancy ; 
at last I succeeded in attaining a complete explanation: — 
W, Weber y in his first absolute-resistance determinatumy found 
for the absolute value of JacobVs resistance-^unit about 8 per 
cent, too small a nurrtber, in consequence of which Quintus 
Idlius's final result could not but come out just as much too 
little. If this error be corrected, the latter value (399*7 m.-k.) 
becomes 431*0 m.-k., a value which, certainly, is somewhat 
greater than that which results from Joule's measurements 
and my own experiments ; but taking into consideration that 
Quintus Icilius has quite neglected the variation of the hori- 

• Pogg. Ann, vol. d. p. 65. 

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188 Electromaffnetic and Calometrie Absolute Measurements. 

zontal component of the earth's magnetic force (which alone 
might make a difference of 2 units in the value of J), that he 
has not reduced the indications of the thermometer he employed 
to the air thermometer (a reduction which might make a dif- 
ference of 4 units)^ and that he used in his experiments very 
powerful currents and very feeble resistances (a procedure 
which must necessarily have been attended with some slight 
errors)^ no great weight will be laid upon this small difference ; 
the previously startling discrepancy is removed. 

It can in two ways be shown fliat W. Weber, as we have 
maintained, found the absolute value of Jacobi's unit of resist- 
ance about 8 per cent, too small. 

Bosscha,in 1856*,determined according to Ohm's method the 
electromotive force of a Danieirs element in absolute electro- 
magnetic measure. His measurements were based on a standard 

of resistance the absolute value of which, 0*607 x lO^Y -* J, 

was obtained by comparison with the above-mentioned copy 
by W. Weber of Jacobi's unit. He found the absolute elec- 
tromotive force of a Daniell's element, in the mean out of 
several measurements, 

= 10-258 xlO^»(°'"^^'" *";"'>*). 
\ sec. / 

This result is proportional to the resistance taken as the basis 
of the measurement ; the error committed in measuring this 
resistance enters into the derived value of the electromotive 
force. 

From a long series of absolute measurements of the electro- 
motive forces of the Daniell element, the details of which shall 
be related in another place, I have found that the lowest value 
of the electromotive force of the Daniell element in absolute 
electromagnetic measure is 

10-96 xlO^'(55^11™:l^ll^*), 
\ sec. / 

that the absolute value of the electromotive force of a Daniell's 
element of the form usually employed is 

11-30 xlO^''( '"^"''°-^T'"'^''-\ 
\ sec. / 

and that the highest value of the electromotive force of a Da- 
rnell's element amounts to 

ll-54xlO^''('°"""-*""^'g^*V 
\ sec.^ / 

• Pogg. Ann, vol. ci p. 617. 



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Mr. W. J. Lewis's Crysiallographic Notes, \Z9 

Which form of Daniell's element Bosscha used, anfortanately 
he does not state ; bat we may assume as extremely probable 
ihat be made use of the form ordinarily employed, to which, 
according to my measurements, belongs the absolute electro- 
motive force 

\ sec* / 

This value is greater, in the ratio of 1'1016 to I'OOOO, than 
that deduced by Bosscha. How, supposing that Bosscha has 
earned out his measurements free from error (a supposition 
which of course cannot be rigorously correct), then the abso- 
lute value of the resistance taken by him as the basis of his 
measurements, u e, the absolute value found by W. Weber for 
Jacobins unit, would be 10* 16 per cent, too little. 

This calculation of the error is based on two somewhat un- 
certain assumptions, briefly indicated above. On this account 
it is a great advantage thiat an error in W. Weber's determi- 
nation of the absolute resistance of Jacobi's unit, in the same 
direction and of the same order of magnitude, can be deduced 
in quite another way. According to W. Siemens the ratio of 
Jacobi's resistance-unit to Siemens's is =0*6618. From our 
numerous and multifariously varied measurements the absolute 

value of the Siemens unit is 0*9550 x 10^^ ( -* ) . Accord- 

\ sec. / 

ingly the absolute value of Jacobi's resistance-unit would be, 

firom our measurements, 0*6320 x 10^^ ( j; while M. 

\ sec. / 

Will. Weber found only 0-598 x lO^C^B^lllEL-^—tliat is, a 

\ sec / 

value about 6 per cent, less than that found by us. 

Hence the absolute measurement by M. W. Weber of Jacobi's 

resistance-unit has turned out certainly from 6 to 10 per cent. 

too little. 

[To be continued.] 

XIX. Crystallographic Notes, 
By W. J. Lewis, M.A.j Fellow of Oriel College^ Oxford*. 

DB. HUGO MULLEK had the goodness, some time ago, 
to send me some crystals of the isomerous compounds 
Qnercite and Inosite, which he had obtained from new sources — 
the former from the leaves of the dwarf-palm (^Chamoerops 
humilis), and the latter from cochineal. 

• Communicated by the CiTBtallological Society, hftTing been read 
October 26, 1877. 



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140 Mr. W. J. Lewis's Crystallograpkic Note*. 

QuercUe. — ^The ciyBtallographj of Quercite has been already 
determined by S^narmont (E^mmelsberg's Dis neuesten For* 
9chungen in der KrystalUChemie) ; bnt it was a matter of 
interest to determine whether any difference either in habit or 
angles conld be found in the crystals obtained from the new 
source. The crystals were found to show the same hemimor- 
phons habit (fig. 1) observed by S^narmont ; and bnt a slight 
change has been made in the elements, which may probably 
be explained by the fact that the crystals obtained by Dr. 
Miiller were very perfect. 

The ciystal is positive ; the optic axes lie in the plane of 
symmetry ; the mean line lies between c and q^ and makes 
an angle of about 20^ with the normal to g^ tne dispersion 
(inolin^e) being considerable, v>p. The angles of the opidc 
axes in air for the red and blue rays were found to be 55^ IV 
and 58° 20^^ respectively. 

Fig. 1. Fig. 2. 





mie forms observed area{l 00},«i{l 1 0}, c{0 1},/{0 1 1}, 
^{101} (fig. 2). The faces of the prism are striated parallel 
to their intersection with a ; and mere is a good cleavage 
parallel to g{\0\}. The following are the elements and prin- 
cipal angles observed and calculated. 

(100, 101)=35° 32^-2, (101,001)=38°80'-8, 
(010, lll)=66°r. 

a:6:c=l: 1'241 : 0-95. 



[ 



ae 

Off 

ff^i 



Calculated 


Observed. 


Sfoarmont 

A 


1 


CMculated. ObeeiW 


•69 '8 
53 201 
•57 36| 


69 5 
53 16J 
57 35 


68 57 68 57 

58 22 aboat 
57 20 


•35 88i 
108 58 


85 82 
108 49| 


85 34 85 82 
108 52 109 5 



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Mr, W. J. Lewises Cryetcdlographic Notes. 



141 



Table (continued). 



Calculated. Observed. ^ 



S^narmont 



Calculated. Obeenred. 



[ 



atn 
mm J 



36 
106 



1/9 

[fi 
Inonte,' 



36 57 

106 

64 39 
54 24 
60 56 

73 5 
106 54: 

-This substance 



56 

64 43 
54 21i 
60 59 

73 8 
106 59i 



106 30 



36 45 
106 29 



crystallizes in colourless, much 
striated prisms, attached by one end to the mass of £he sub- 
stance. The striations on the planes lyin^ in the prism-zone 
rendered it impossible, even in the most dehcate needles, to get 
reliable measurements of the angles in this zone. The prisms 
were terminated by four small planes, {101}, {101}-, and 
{0 1 2}n of which the former was most largely developed, some- 
times even to the exclusion of the other planes. The crystals 
were extremely friable, and lost a portion of their water very 
readily — ^properties which rendered the examination difficult 
and prevented the determination of their optical character. 
The opposite faces in the zones were in all cases considerably 
displaced, so that there was always a divergence from the zone 
and from 180^ in the sum of the angles between them. The 
foUowiuff elements and measurements can therefore only be 
regardea as approximate. 

Fig. a Fig. 4. 





mj 



f. 




The system is oblique. The forms are 6{0 1 Of, m{l 1 0}, 
p{210j,{410^i{101},<{101},*{012}(fig.4). 



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142 Mr. W. J. Lewis's Cryttattographie Jfotet. 

(100, 101)=40O51|', (101,001)=28°27f', 

(010, 111)=62''45§'; 

o: 6: c=l-0802: 1:0-7869. 

Oslcnlated, Obterved. 

It 71 O' 70 34ito70 27 

Ik 34 24i 34 36 „ 34 14 

tk 46 15 46 11 „ 45 54 

rbm 44 42 44 50 „ 44 36 

hp 63 Hi 63 13 „ 62 52 

6(410) 75 49i 76 „ 75 45 

Unm, 89 24 99 37 

rml 57 51f 57 56 

Iml 122 8| 121 49i 

m,t 74 49 74 58 „ 74 52 

m,t 105 11 105 6 ,,105 10 

mk 61 24j^ 61 52 „ 61 34 

mk 118 35| 118 10 

m.k 89 17 

hi 90 89 53i 

Vhk 69 47i 69 32 „ 70 3^ 

U*, (over 001) 40 25 40 13 

Jordanite. — On a crystal of blende from the Binnenthal in 
the British Moseom two small crystals, the one of Jordanite, 
the other of Binnite, are implanted. The former, on measare- 
ment, was found to be a combination of the forms {001}, 
{119}, {113}, {225}, {112}, {110}, {013}, {025}, 
{012}, {0 2 3}, {Oil}, {312}, {311}, {310}. Of these 
the forms {2 2 5}, {0 2 5}, {0 2 3}, {31 2}, {310} are, I be- 
lieve, new. The middle index in these symbols corresponds 
to the brachjdiagonal usually denoted by the letter y and the 
parameter b. This arrangement is not to be confounded with 
that of Professor vom Bath, in which b corresponds to the 
makrodiagonal and a to the brachydiagonal. The angles be- 
tween some of these planes observed and calculated from the 
elements, c: ^0=65^0'; ^ox^o^bQP 49', given by Prof, 
vom Batii are : — 



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Mr. W. J. Lewis's Cry$t<Mographio Notes. 143 



T. Bath's 
notation. 



-001:013 c:\d 

001:025 

001:012 c:\d 

001:023 
L001:011 c:d 



Calculated. OlMerred. 


51 33 51 3^ 

56 301 not determined. 

62 eX 62 6 

68 20| 68 23 

75 lO; 75 6 



[ 



001:312 74 24A 74 15 

001:311 cm 82 3| 81 47 

001:310 90 89 65 

"312:112 29 32 29 30 

.112:012 io:id 25 24^ 25 27 



The plane (112^ was the largest plane on the crystal, 
(001) the next. All the other planes were small ; and some 
ihin twin laminae were observed mtersecting the zones [0 1, 
310] and [001,112]. 

BinnUe, — ^This mineral has occupied the attention of several 
mineralogists, a summary of whose work on it is given by 
Hessenberg in his Min. tfotizerty ix., where he describes a very 
beautiful specimen in his possession. Kenngott, after an ex- 
amination of the crystals in Wiser's collection, came to the 
conclusion that the mineral was hemihedral, a conclusion com- 
bated by von Waltershausen. After a careful study of the 
distribution of the faces on his crystal, Hessenberg^ comes to a 
conclusion opposed to that of Kenngott ; for although the 
forms {111}, {211}, |321}, {411}, and {10, 1,1} were 
incomplete, he found tnat the faces of {1 1 1}, {2 1 1}, and 
{3 21} were present in an irregular manner. He has made 
no remark, however, on the fact that the faces of {4 1 1} and 
{1 0, 1, 1} are present in adjacent octants only. 

In the exammation of the specimen in the British Museum, 
especial attention was paid to the distribution of the faces of 
the different forms. It consists of two crystals united together 
in parallel positions, or possibly of one crystal whose free de- 
velopment has been prevented at one point by the presence of 
some body, and has the forms {1 1 0}, {2 1 1}, {1 0}, {1 1 1}, 
{3 2 1}, k{4. 1 1}, k{& 1 1}, k{1 1 1}, k\\0,\ 1}, and k{2 3 3}, 
of which k{111) is new. The forms {1 1 0}, {2 1 1} are well 
and about equally developed ; the others are subordinate. The 
number of octants which could be examined was six; so that 
the question of the hemihedrism could be more thoroughly 
tested than it was by Hessenberg, who was only able to ex- 
amine four. The forms {110}, {211} were well developed 
in adjacent octants, and are therefore holohedral. The forms 



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144 Prof. J. Emerson-Beynolds on the 

{i 1 1}, {6 1 1}, {7 1 1}, U 0, 1 1}, and {2 3 3} were found in 
alternate octants onlj^ and are consequently hemihedral. The 
faces of {3 2 1} were for the most part badly developed^ and 
did not permit of any certain conclusion being drawn. Hes- 
senberg found a plane of the form in each of two adjacent 
octants which excludes a hemihedrism with inclined faces. I 
believe it, from my observations, to be holohedral. A further 
examination of such cirstals as are to be found in the various 
collections might possibly set the question of the hemihedrism 
of the mineral at rest, and would certainly be interesting. 



XX. Short Reports from the Chemical Laboratory of Trinity 
Collegej Dublin, By J. Emebson-IIbykglds, M.D.y Pro- 
fessor of Chemistry^ University of Dublin'^, 

No. 5. On the Rapid Estimation of Urea. 

A DISTINGUISHED physician, who wished to make 
frequent determinations of the urea dailv excreted by 
a patient, requested me to devise a method which would enable 
him to make the desired estimation — (a) rapidly, (6) with suf- 
ficient accuracy for ordinary clinical purposes, (c) with simple 
and easily constructed apparatus, and (d) without the use of a 
balance or of any measuring-vessels other than the fluid-ounce 
and minim measures which a medical man is in the habit of 
employing. 

This interesting practical problem was solved in the manner 
I shall presently describe ; and the results obtained by the use 
of the method devised have been so satisfactory as to lead me 
to expect that it may be found generally useful where a high 
degree of accuracy is not desirea. 

1 propose, however, before concluding this paper, to describe 
a less simple plan for the estimation of urea than that just 
referred to, but one which is capable of afibrding results of 
greater precision. 

In both the methods mentioned I take advantage of the now 
well-known reaction of sodic hypobromite with urea. When 
a strongly alkaline solution of sodic h^obromite is added to 
a liquia containing urea, the latter sufiers rapid decomposition 
into water, carbonic anhydride, and pure nitrogen gas. The 
carbonic anhydride is not evolved as gas, but is absorbed, with 
formation of sodic carbonate, bv the free alkali of the liquid 
used to effect decomposition ; the nitrogen is evolved in the 
gaseous condition, and its bulk determined either indirectly or 

* From the Scientific Proceedings of the Royal DuUm Society. Com- 
municated by the Author. 



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Bapid EHimatum of Urea. 145 

direoUj, the volume of nitrogen produced thns serving as a 
measure of the nrea from which it was derived. 

The equation which expresses the change just referred to is 
the following : — 

CCy'N, H4+3(NaBrO) + 2(NaOH)=3NaBr+Na,CO, 

"-r^ ' , Sodic^ +3H,0+2K 

Urea. nypobzomite. 

^ The use of calcic hvpochlorite, or solution of " chloride of 
lime," in effecting a smiilar decomposition was pointed out hj 
Dr. E. W. Davy* ; and it has been recently shown by Yvon f 
that the hypochlorite used by Davy is more effective than the 
sodic hypochlorite^ but it cbes not evolve the whole of the 
nitrogen and is irregular in its action. Knop, and after him 
Hufiierf^ and many others, have shown that the sodic hypo- 
bromite is greatljr to be preferred to any of the hypochlorites, 
as the decomposition of urea is almost complete, and progresses 
regularly and rapidly without the aid of heat : hence I use 
the hypobromite as the basis of the plan of operating now to 
be described^ and in this respect agree with Hiifher, Bussell 
and West, B. Apjohn, Blackly, iJupr^ [and with Simpson 
and O'Keefe §] in the methods they nave proposed for tuea- 
estimation. 

The different methods devised by the above-named chemists 
all serve for the direct measurement of the volume of nitrogen 
evolved during the action of the hypobromite on urea, and 
involve the use of specially graduated tubes for the reception 
and measurement of the pure gas. My plan is essentially dif- 
ferent, as the gas evolvea, which is scarcely soluble in water ||, 
is maae to displace its own volume of that liquid, and the latter 
is then easily measured in any ordinary vessel^ such as a tall 
and weU-graduated drachm measure. 

The apparatus may be most conveniently described as con- 
sisting of two distinct parts — A, the generatinff-vessel (see 
annexed woodcut, fig. 1), and F the small ^as4iolder, nx>m 
which water is expelled by the nitrogen entenng from A. 

Gas^enerating Vessel. — ^This isan ordinary two-ounce wide- 
mouthed bottle, fitted with a good india-rubber cork pierced 
with three holes. Through one of these holes the gas-delivery 
tube E passes, and through another the small piece of bent 

• Jounial of the Royal Dublin Society, and Phil. Mag. [IV.] voL viL 
p. 403. 

t JowTfuU de Pharmade et de Oiimte, [4] yoI. xziv. 

I Journal fUrprakHBe^e Chemie, [2] yoL iii. p. 1. 
§ Published since this paper was read. 

II According to Bunsen. water dissolyeB only 0*01478 of its volume at 
the mean temperature and pressure (Bunsen's < Gasometiy/ p. 286). 

FhU. Mag. S. 5. Vol. 5. No. 29. Fa>. 1878. L 



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146 Prof. J. Emerson-Reynolds en tlie 

glass tube C. The heat afforded by a spirit-lamp suffices for 
bending these tubes from straight pieces, and for tte oonvereiou 

Fig.l. 



of an ordinary bulb-pipette, capable of holding rather more than 
one fluid-ounce, into a vessel of the form B. 

The delivery- tube of the pipette is first passed through the 
remaining hole in the cork, and the end of the tube then drawn 
out and recurved, as shown at c ; the tube above b is bent so 
far down as to admit of its being connected by means of an 
india-rubber tube with the outer extremity of C. At D the 
india-rubber tube is securely clipped by a small artery-forceps 
with broad jaws. When the cork carrying the tubes iust 
described is secured in the bottle, the generating-vessel is 
complete. "When an estimation is in progress the bottle A is 
placed in a tumbler, T (or beaker), containing cold water at a 
temperature of 52° F., as nearly as possible. 

The Gas-Deceiver, — ^Tlus is easily constructed from a large 
pipette whose bulb F is capable of containing about three fluid- 
ounces. The tube/ is cut off so as to admit of being securely 
joined to the tube E of the generating-vessel by means of an 
india-rubber connector. The delivery-tube is then bent, as 
shown, and at the point H a little hole is made. A groove 
cut in a block of wood g receives the bent tube of the little 
gas-holder, which is then easily secured in its place by any 



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Rapid Estimation of Urea. liT 

suitable cement — common sealing-wax^ for example. Thns, 
with the aid of the two pipettes^ cork, and tnbing, which can 
be easily procured through a druggist for about 3s, ^ a medical 
man can construct his own ureometer*. 

When in use the block g is secured to the board S^ on which 
the beaker T stands held bj the wire W. 

Mode of tuing tlie Apparatus, — The vessels A and F are 
disconnected, and F filled with water until it overflows and 
the excess has ceased to drip from the tube under H. The 
cork is removed from the bottle A, and two fluid-drachms of 
the liquid to be tested measured off in a tall minim-measure, 
and then poured into A ; one drachm of water is next used to 
rinse the liquid adhering to the sides of the measuring-glass 
into the bottle A : the total volume in A therefore should 
measure about three drachms f. For a reason which will 
presently appear, it is desirable that no more water than one 
drachm should be employed. If a pipette delivering two 
drachms be used, a drachm of water should be added ; but the 
pipette need not be rinsed with it. The next step is to fill the 
pipette B with the reagent which evolves the nitrogen of the 
urea. For this purpose a suitable vessel (a wine-glass for 
example) is filled with the hypobromite liquid X ; ^e forceps 
D is removed from the india-rubber tube, but is placed 
dose at hand, and a piece of vulcanized tubing, five or six 
inches long^ attached to the end of the glass tube C ; suction 
is then applied by the mouth when the curved end c of the 
pipette is immersed in the hypobromite. The pipette is thus 
easily filled by suction vrith the re-agent up to the mark i. 
The forceps D is next applied to the connector, as shown, . 
before the lips are withdrawn from the india-rubber tube at- 
tached to G ; the suction tube may then be removed from 0, 
as the liquid is retained in B by atmospheric pressnre, pro- 
vided D pinches the tube well. Having washea the end e by 
ponring a littie water over it, the cork carrying all its apparatus 
is securely inserted in the bottle A, the latter placed in the 
beaker T containing enough water to cover the cork when A 
is pressed down, and the tube E securely connected by the 

* Meaers. Testes & Son, of Dublin, sapply a neat fonn of my apparatus 
ready for um. 

t The measure used should be good, the two-drachm and two-ounoe 
Teasels agreeing with each other. The amount of reliance which can be 
placed upon the results depends in great part on the accuracy of the 
measures. 

t This solution is prepared as follows : — ^Dissolre 4 ounces of the solid 
caustic soda of the shops in 10 fluid-ounces of water. When the soda has 
dissolved and the liquid cooled to 60^ F., add gradually 1 fluid-ounce of 
bromine. The test solution is then ready for use. It snould be kept in a 
cool place, and away firom the light 

L2 



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148 Prof. J. Emerson-BeynoldB on the 

tightly-fitting indiarnibber tabe with jT. While connecting 
the generator and receiver a little water is necessarily expelled 
from the tube beyond H; bnt this water is thrown away, and 
the dry two-ounce measure, I, then placed under the spout. 

Up to this point the hypobromite has not been allowed to 
come into contact with the urine ; but now, on remoying the 
forceps D,the hypobromite flows out from c and rapidly mixes 
with the urine, the urea of which yields up its nitrogen gas vrith 
effervescence. As the gas evolved has no exit save through E, 
it displaces from F its own volume of water, which falls into 
the vessel I, and can then be measured when no more water 
is expelled. The effervescence ceases after five or ten minutes, 
according to the temperature. 

It is essential to ffood measurement that the pressure within 
the apparatus should be the same at the end as at the beginning 
of the experiment ; in order to secure this, the simple plan is 
adopted of placing a wedge under the board S at the end in- 
dicated, which is thus so tilted that the eye placed at a point 
a littie below D, and looking immediately above the surface of 
the water in F, can just see the bend of the tube under H. 
When the pressure wimin and without has been thus equalized, 
'the amount of water expelled is the measure of the nitrogen 
evolved in A ; for we may in a test of this kind neglect the 
extremely minute proportion of the nitrogen whicli has been 
dissolved by the water. 

When it is desired to correct for temperature and pressure 
by means of the usual formula, it is now necessary to disconnect 
E and /, and to pass the bulb of a small thermometer through 
/into the gas over the water in F ; after a minute or so me 
temperature may be read off and recorded, and the barometric 
reading made at the same time. In ordinary clinical ex- 
periments, however, the correction for temperature may be 
neglected when a thermometer in the room stands near to 52^ 
F. The neighbourhood of a fire or stove must be avoided in 
making the estimations of urea. 

In mecuuring the vxUer expelled we may either read off the 
volume in drachms or sixths of a drachm ; but since ordinary 

Slindrical two-ounce measures are rarely graduated to less 
m half-drachms, the beet plan is to pour ue excess over a 
definite number of drachms into a tall two-drachm measure, 
bearing in mind that every ten-minim division represents the 
sixth of a drachm. 

I find as the results of a large number of direct experiments 
with a standard solution of pure urea, some of which will be 
given further on, that one grain of urea producee eujfficient gae 
at a temperature of 52^ F. and a barometric preesure of 30*06 



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Rapid EsHmoHon of Urea. 149 

inches to exj^l 6| drachms of watery the volnme of liquid in the 
bottle A being toree drachmfl; and the hypobromite added ten 
drachms. 

It may be mentioned that measures of capacity need not be 
employea in the detenninations of urea, as the water expelled 
may be received in any suitable vessel which has been pre- 
viously weighed. At the end of the experiment the vessel and 
expelled water are weighed. When the estimation was made, 
mider the conditions above named, one grain of urea was found 
to expelj as a meany 365 grains of water by weight. This 
number is easily remembered, as it happens to be identical with 
the number of d^s in a year. 

Effect of the Degree of IHlution upon the Determination of 
Urea. — ^An apparently tnfling observation led me to examine 
tiie effect of dilution upon the yield of nitrogen obtainable from 
a constant weight of urea ; ana the results arrived at are stated 
in the Table given below. 

The quantity of pure dry urea operated with in each of the 
following experiments was 2*222 CTains ; and the same volume 
(», e. ten fluid-drachms) of a single sample of freshly prepared 
sodic hypobromite was added in each case. The experiments 
were completed within three and a half hours : ana care waa 
taken to avoid changes of temperature as much as possible : 
hence, while the barometer remained steady at 30*06 inches, 
the temperature varied within such very narrow Umits (be- 
tween 50^ and 52® F.) that corrections for alterations of 
volume were unnecessary, as extreme accuracy in the measures 
of the water expelled was not attainable with the vessels ad- 
visedly employed, as I desired the results to be of such a kind 
as a medical man could easily obtain in his own study. 

Table. 



No. of 


Pure dry urea 


Volume of water 


Tolame of 


experi- 


used in 


used to diasoWe 


water expelled 
fromf. 


ment. 


experiment. 


urea in A. 


1. 


2-222 grains. 


drachm. 


16i draohms. 


2. 


n 


1 „ 


16 


3. 


n 


2draohms. 


1*» „ 


4. 


»f 


2 ., 


14* » 


6. 


»» 


3 ,. 


14| „ 


6. 
7. 




S „ 

4 M 


14| „ 
14| » 


8. 


n 


6 „ 


Lost. 


9. 


99 


6 » 


14 + „ 


10. 
11. 




I : 


1S< „ 


12. 


M 


9 „ 


13f + „ 
131 + ., 


13. 


»f 


10 „ 



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150 Frof. J, Emerson-Beynol4s on the 

The weight of urea taken for each experiment is capable of 
affording a volmne of moist nitrogen gas at the temperatnre 
and pressure above stated^ which would expel 15| drachms of 
water. The maximum volume obtained from that weight of 

Eure dry urea was 15Jr drachms. Thus there is a minimum 
>8S of 0*3 per cent. The maximum observed loss in the fore- 
going experiments amounted to 14*9 per cent., and occurred 
m the experiment in which the above-named weight of urea 
was dissolved in ten drachms of water. The loss within the 
above limits is tolerably regular, as the volume of nitrogen is 
diminished by ^ of a drachm (nearlv) for each drachm of water 
added to the urea in the decomposition-vessel A. 

The loss of nitrogen referred to is, doubtless, due in part to 
solution of the gas; K)ut it is chiefly attributable to the regular 
diminution of the strength of the oxidizing agent used, 
the hypobromite solution, and to a corresponding increase in 
the extent of secondary changes which are known to occur in 
the diluted liquids, and which involve a loss of gaseous ni- 
trogen. Much of the error arising from the latter cause is 
avoided by adopting the plan of employing a constant volume 
of liquid ; hence the recommendations already made that two 
drachms of urine should be measured into the bottle A, and 
the measure rinsed out with not more than one drachm of 
water. The total bulk of liquid in A ought then to measure 
as nearly as possible three drachms. Even when the sample 
to be testea is measured with a pipette, it is well to add one 
drachm of water from an ordinary measure in order to bring 
up the total volume of liquid to the amount recommended. 

When the simple precautions are taken which I have already 
mentioned, the little apparatus described in this paper will en- 
able a considerable number of estimations of urea to be made 
with rapidity, and with sufficient accuracy for ordinary clinical 
purposes. When very precise determinations are required, 
Liebig's process must be resorted to, as all the methods in 
which hypobromites or hypochlorites are employed are liable 
to the errors pointed out above ; the accuracy of the results 
is also affected by the action of tiie reagent used on uric and 
hippuric acids, creatinine, and other nitrogenized compounds. 
On the other hand, when we desire to ascertain the total 
amount of nitrogen excreted by the kidneys, it is necessary to 
resort to the nrecise method of estimation which I communi- 
cated to the Surgical Society of Ireland*. 

* Fid* Medical Press and Circular, May 13th, 1874, p. 402. 



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Rapid EiHmcUwn of Urea* 151 

Estimation of Urea by direct Determination of the Nitrogen Gas 
evolved by Sodic Hypobromite. 

The piece of appara* ^^* 2. 

ins now to be described 
was exhibited ata meet- 
ing of the Scientific 
Qab in 1871, and has 
proved most oseful for 
the estimation of urea 
by the hypobromite me* 
thod, and, with a little 
modification, for the 
estimation of carbonic 
acid in carbonates, and 
for other similar pur- 
poses. I shall only re- 
fer at present to its use 
in nreometry. In this 
apparatus the nitrogen 
evolved is directly mea- 
sured as ^as under con- 
ditions which admit of 
verv accurate determi- 
nations of volume in 
cubic centimetres. 

The apparatus is 
shown in section in 
fig. 2. The stand A 
supports a tall glass 

Slinder B. Through 
e larffe india-rubber 
cork which closes the 
lower opening of the 
cylinder the U-tube o 
is passed, great care 
being taken to avoid 
breaking the small T- 
connector o. The outer 
limb of the U-tube is 

Erovided with a glass 
ipT. The limb within 
the tall glass cylinder 
is sufficiently wide to 
contain 150 cub. cen- 

tims. in the expanded : 

portion^ which; in my 

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152 On the Rapid Estimation of Urea. 

apparatus measures 60 oentims. in lengiih. The graduation 
cannot be conveniently carried bejrond fifUis of a cubic cen- 
timetre. At the point snown an india-rubber tube ff is attached, 
which can be closed at will either bj a good clip or bj a 
stopper of glass rod. The glass side-tube c serves to connect 
the measunng-4ipparatus in the manner shown with the ffene- 
rating-vessel D, which is a long and wide glass tube placed 
wittnn tile cylinder. The glass T-tube E is connected by 
means of rubber tubing with c, while one limb passes througn 
the india-rubber cork of D^ and the other is connected by 
another piece of rubber tubing with the fine tube of the long 
pipette F (of about 20 cubic centims. capacity) which pro- 

^ects through the cork. This connexion must be suffidentiy 
ong to admit of the clip being applied as shown. 

'fno large glass cylinder B is filled with water in order to 
maintain a steady temperature, the value of which can be 
known by means of a thermometer immersed in the water. 

A determination is made with this apparatus in the following 
way: — Having disconnected the T-tube E from c and the cUp, 
the generating-tube D is taken out of the water of the cylinder, 
the cork carrying the pipette, &c. withdrawn, and then 5 cubic 
centimetres of the urea solution introduced into the tube D. 
Before replacing the cork the pipette F is filled with hypo- 
bromite solution by suction above E, while the small glass 
tube opening on the underside of the cork is closed by a 
finger ; the dip is then applied. The exterior of the pipette 
is now washed with a littie water, and the cork, with the ap- 
paratus attached, is then replaced in position, the tube D 
again immersed in the water of the large cylinder, and the 
connexion between E and c securely maae. Before making 
the connexion the water in the graduated tube should stand ai 
the zero of the scale ; but after making the joint the pressure 
witiiin the apparatus is usually greater than that without. As 
the air in the tube D cools down to the temperature of the 
surrounding water, contraction takes place ; but should the 
water not return to the zero, equilibrium is at once restored 
by opening the fine india-rubber tube g for a few seconds, 
and then dosing in such a manner as to prevent any possible 
escape of gas. 

Tne hypobromite is brought into contact with the urea solu- 
tion by removing the clip from the india-rubber tube connected 
with me pipette ; the reagent then falls from a considerable 
height and mixes thorougnly with the liquid at the bottom of 
the tube D. Nitrogen is evolved and displaces water from e, 
the water being maintained at the ^ame level in both limbs of 
the U-tube by allowing the liquid displaced to run off by 
means of the tap T. When the evolution of gas has cease(^ 

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.Notices respecting New Books. 153 

ihe water-level is adjasted hy means of the tap, and the volume 
of gas produced in uie reaction then read off on the graduated 
tube c ; the temperature of the water in the cylinder B is then 
ascertained; as well as the height of the barometer at the time. 
From the data thus obtained, the volume of dry nitrogen at 0^ C. 
and 760 millims. can be easily calculated by the usual formula. 

XXI. Notices respecting New Books. 
JSasperimental Researches in Pure^ Applied^ and Physical Chemistry. 

By E. Frankland, PKD.t D.CJj.^ F.EJS. London : John Van 

Voorst. 1877. 
T^E. EBANKLAND has laid his chemical brethren under a 
-^ great obligation by the publication of his researches in a col- 
lected and classified form. That obligation may be best repaid by 
the determined efforts of other chemists to explore those fields cA 
knowledge which have been left untrodden by the authcxr of the 
work now before us. 

The researches of the South-Kensington Professor extend over 
a period of about thirty years ; they are arranged in three sections 
— ^Pure, Applied, and Physical Chemistry. 

In the myision of Pure Chemistry, Dr. Erankland has rendered 
himself famous by his researches upon the Alcoholic mdicals, 
Organo-metallic bodies, and Synthesis of the Acids of the Lactic, 
Acrylic, and Acetic series. At the time when the earlier of these 
investigations appeared, the chemistry of the Carbon compounds 
was in a state of confusion : many facts had been collected, but 
little breath of life had been breathed into these dry bones. Lau- 
rent and Gerhardt had scarcely made known the results of the appli- 
cation of their brilliant classificatory powers to the facts of organic 
Chemistry. The theory of radicids had indeed been advanceii by 
Liebig and Kane ; but the unscientific use of hypotheses concerning 
the nature of organic compounds was yet, for the most part, domi- 
nant. Berzelius and his dualistictheoiTwere masters of toe field. In 
terms of this theory, Berzelius viewed Acetic Acid as a conjugated 
compound containing the groups C, H, and C, O, (old notation). It 
is worthy of remark that the exceedingly imperfect and one-sided 
theory of Berselius, as applied in the above-cited case, should 
have furnished an idea which, when worked out by Dr. Frankland 
in his researches upon the *' Conversion of Cyanogen into Oxatyl,'' 
led to results of much importance in advancing the more complete 
and more probable theories of modem Chemistry. The Badical theory 
of Liebig found great support by the publication of Frankland's 
memoirs upon the " Isolation of the AlcohoUc Badicals." In at- 
temptmg to isolate the radicals Methyl, Ethyl, and Amyl by the 
action of metals upon the iodides of these bodies, Frankland ob- 
tained results which he then regarded, and which, judging frcHn the 
introductory remarks in the present volmne, he seems stul inclined 
to regard, as proof of the actual isolation of these radicals. Frank- 
land pointed out the analogy between Hydrogen and the radicals of 
. the Alcohols ; and, if the molecular formula of Hydrogen be H„ he 



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154 Notices respecting New Boohs. 

argued that the molecular f ormulsd of Methyl and Ethyl should be 
(CH,), and (C,Ha), respectively. But the hydrides of these 
radicals haye respectiyely the formulae CH,H and 0,11,11: 
Schorlemmer has shown that 0, H, H is identical, not isomeric, 
with Frankland's Methyl (CH,),. Erankland's own investigation 
upon the action of Chlorine upon Methyl (?) and upon Ethylic 
hydride, led him to regard these bodies as isomeric only. We 
had supposed that Schoriemmer's investigations had finally settled 
this point ; but from what Erankland says in the present volume, 
he, at least, does not appear to regard the evidence as perfectly 
conclusive either way. Had the researches upon the Isolation of 
the Alcoholic radicals been productive of no other effect than to 
incite other chemists to attack the problems which they enunciated, 
they would have deserved the warmest thanks of every student of 
chemical science. But they did more than this : in these researches 
a great number of new and most important facts were added to 
the science ; new instruments and new methods of research were 
introduced to the chemist ; and new generalizations were advanced, 
which have most powerfully aided in the advancement of the true 
scientific study of the carbon compounds, notwithstanding that some 
of them have been unable to withstand the criticism, and haye 
faUed to completely explain the facts amassed by later investigators. 

The analogy between Erankland's Alcoholic radicals, (CH,),, 
(CjHjX, &c., and Hydrogen (H^) doubtless led to important 
generalizations ; it may, however, it seems to us, be pushed too 
far. If the molecule be the smallest part of a body which exhibits 
the properties of that body, then (CH,), and (CjH,), may be the 
molecular formulie of methyl and ethyl respectiyely. In entering 
into chemical action, these molecules may be regaraed as splitting 
np each into two atoms, CH, and Cj H^, just as we regard the 
molecule H^^ as being divided into H H before a chemical combina- 
tion takes place between hydrogen and another body. But if this 
be a true hypothesis concerning the molecular and atomic consti- 
tution of Methyl and Ethyl, it would almost necessitate the view 
that, after aU, transmutation or something analogous thereto is 
actually a fact, because the atom (if one may speak of the atom of 
a compound) CH, combines with another atom CH, to produce 
the same compound as is formed when the atoms C^H, and H 
combine together. 

At the beginning of the volume now before us is placed a paper^ 
first published some ten years ago, on Notation. We cannot but 
regard it as a mistake on the part of Dr. Frankland that in collect- 
ing his researches he has maintained that peculiar notation which, 
with its thick and thin letters, with its small O's and large C's, 
has never met with favour among chemists in general, and the 
presence of which in the present work must surely somewhat 
narrow the influence for good of these memoirs. This notation is 
founded on many somewhat sweeping generalizations : it really, 
we think, assumes an amount of knowledge which we do not pos- 
sess ; and in doing this it tends, we are afraid, rather to hinder 
than to advance the progress of true inquiry. 



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Notices respecting New Books. 155 

Dr. Frankland is an upholder of the doctrine of yarying valenoj. 
In his paper on Notation he brings forward the unhappy example of 
Ammonium Chloride as illustratiYe of compounds in which 
Nitrogen is pentavalent: in Nitrous Oxide he says Nitrogen is 
monovalent. Surely such statements as these are far too rash: 
we do not know the molecular formula of sal ammoniac; and 
we are much more justified in saying that nitrogen is trivalent in 
nitrous oxide, tlian in averring, as our author does, that the same 
element is trivalent in nitric oxide. Variation in valency seems to 
take place by leaps : a trivalent element may, it seems, sometimes act 
as monovalent, but rarely, if ever, as a divalent element. Such facts, 
says Frankland, " can be explained by a very simple and obvious 
assumption, viz. that one or more pair of bonds belonging to one 
and the same atom of an element can unite, and, having saturated 
each other, become, as it were, latent." We fail altogether to see 
that this *' simple assumption '' eocplains the facts in any way ; it 
merely restates them. On pp. 24, 25 there appears a most unfor- 
tunate list of mineral compounds formulated in accordance with 
Dr. Frankland's system. The formulsB there given are pleasant 
to the eye ; but that is all. Por the most part they really have 
no Icnown foundation in fact. 

Section II. includes those papers v^hich have been contributed 
by Dr. Frankland to Applied Chemistry: these papers chiefly deal 
with subjects connected with Gas and Water. The practical re- 
sults of the work collected in this section are known to all. We 
are certainly largely indebted to the author of these researches for 
many improvements in our lighting and in our water-supply. The 
memoirs now collected form a good example of the benefits which 
always accrue when science is adequately applied to technical sub- 
jects. They may furnish a powerful argument to those who are 
ever ur^g Government to expend a larger portion of the nation's 
money in investigations undertaken by really qualified scientific 
men into those problems of applied science which every one 
acknowledges must be solved, but which can only be solved by 
national effort. 

The papers upon Wat-er-analysis recall the controversy between 
the upholders of the system of Wanklyn and those of the sys- 
tem of Frankland. Such a controversy should nerer have oc- 
curred : happily there are signs that the bitterness is dying away ; 
let us hope that the action of time will be as the action of a flow- 
ing river upon the subject which has engendered this hostility, 
and that before long the clamour may be remembered only as a 
dream of *' previous sewage contamination." 

In the Third Section we are presented with the papers on Phy- 
sical Chemistry contributed by Dr. Frankland to science: these 
papers, for the most part, contain the record of work done or sug- 
gested during holiday excursions. "The Influence of Pressure 
upon Combustion," the "Spectra of Gases and Vapours," the 
" Source of Muscular Power," and " Climate " form the main sub- 
jects dealt with in this section. The results of Dr. Frankhmd's 
researches in thene various fields have passed into the common stock 



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156 Geological Society :^^ 

of knowledge. Some of these results have been called in ques- 
tion, more particularly those concerning Elame. The recent re- 
searches of Heumann have, we think, shown that Frankland was 
much too sweeping; in many of his assertions regarding the lumi- 
nosity of hydrocarbon flames, and have proved that those flames do 
indeeid owe their luminosity to the presence of solid matter. ^ ever- 
theless Prankland's experimental work on Flame remains a monu- 
ment of what may be done even in the time given to recreation by 
a determined and loving student of Nature. 

The papers on Muscular Power embody the results of much 
accurate and exceedingly valuable work ; they are of interest both 
to the chemist and to the physiolo^st. 

The publication of these collected researches cannot but increase 
the fame which their author has already earned ; it cannot but aid 
in the advance of scientific chemistry by setting before the student 
an example of what may be accomplished by steady honest work, 
and by instructing him, both by precept and example, in the path 
of true scientific research. The best return which can be macb to 
Dr. Frankland is that every worker in the field of chemistry should 
determine that he too will Drove himself not unworthy of that 
study to which he has devotea himself. 



XXII. Proceedinffe of Learned Societies. 

GEOLOGICAL SOCIETY. 

[Continued from p. 74.] 

December 6, 1877.— Prof. P. Martin Duncan, M.B., F.R.S., 
President^ in the Chair. 

THE following communioatioiis were read : — 
1. '' On the Building-up of the White Sinter Terraces of Boto- 
MiihiUiii, New Zealand." By the Bev. Bichard Abbay, M.A., F.G.8. 
The author described the structure and mode of formation of the 
so-called '< White Terrace " of Boto-M4hkii, which is produced by 
a deposit of silica from the wa£er of a geyser situated on the side of 
a small hill of rotten rhyolitio rock, about 100 feet above the 
surface of the warm lake (Boto-m^hin4), into which the water from 
the geyser finally flows, and the foot of the siliceous terrace projects. 
The geyser-basin, which is between 300 and 400 feet in circum- 
ference, has steep walls, broken through only on the side towards 
the lake, where the water pours down to form a succession of 
terraces, which are really shallow basins, over the outwardly in- 
clined edges of which the water flows, depositing the dissolved silica 
in a white subflooeulent form on the edges and bottoms of the 
basins in proportion as the water cools. The author showed how 
this arrangement produced the peculiarly formed siliceous deposit of 
the terraces, and that, as the growth of the latter is evidently up- 
wards as well as outwards, it seems probable that the geyser-pipe 
has slowly worked its way up the hill by the solvent action of the 
heated water, from the level of the lake to its present elevation. 



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On the Dimetian and PMdum Roehs of PembrokeBhire. 157 

2. "Additional notes on the Dimetian and Pebidian Books of 
Pembrokeshire." By Henry Hicks, Esq., E.G.S. 

The additional facts communicated by the author show that at a 
distance of about 10 miles to the east of the Dimetian axis of St. 
David's there is another ridge of these rocks, which also runs nearly 
parallel with it. This is also flanked by Pebidian and Cambrian 
rocks, and made up of rocks like those in the St.-Dayid'8 axis. 

The Dimetian formation, so far as it lb at present known, consists 
chiefly of the following rocks : — 

1. Quartz porphyries, containing frequently perfect quartz crys- 
tals (double pyramids), subangular masses of quartz, and crystals of 
febpar in a fdspathic matrix. 

2. Pine-grained greyish quartz-rocks, rery compact, and inter- 
stratified with the above. 

3. Ashy-looking shales of a dull green colour, sometimes highly 
indurated, but usually showing lines of lamination. Microscopi- 
cally these show basaltic characters, and are probably greatly altered 
interbedded basaltic lavas. 

4. Compact granitic-looking rocks. 

5. Quartziferous breccias. 

6. A series of compact quartzites and crystalline schists, inter- 
stratifled with green and purple altered basaltic lavas with a slaty 
and schistose foliation, and with some dolomitic bands. 

Of the Pebidian formation new areas were added, and the por- 
tions described in the author's previous paper were further extended, 
and details as to the chief mineralogic^d characters given. At the 
base of the series resting unconformably on the Dimetian is seen an 
agglomerate composed of large ang|ular masses of a spherulitic fel- 
stone, pieces of quartz and quartzites, indurated shales, crystalline 
schists, &c., cemented together by a sea-green matrix of felstone. 
These are followed by conglomerates of the same materials, which 
are again succeeded by indurated shales, often highly porcellanitic 
in character, with a oonchoidal fracture. 

These are followed by a thick series of silvery- white and purplish 
shales and green slates, alternating with fine and rough ashes, often 
conglomeratic, homstone breccias, fefttone lavas, &c. 

The series, as exhibited at St. David's, has a thickness of over 8000 
feet ; and as it is everywhere, so far as yet seen, overlapped uncon- 
formably by the Cambrians, it may probably be of much greater 
thickness. It evidently consists very largely of volcanic materials, 
at first derived from subaerial, but afterwards from submarine vol- 
canoes. These materials, however, were also undoubtedly consider- 
ably aided by sediments of a detrital origin. 

The whole series shows that the sediments have undergone con- 
siderable changes, but yet not sufficient to obliterate the original 
characters, and the lines of lamination and bedding are usually 
very distinct. That they were altered nearly into their present 
state before the Cambrian sediments were deposited upon them 
is clear from the fact that the pebbles of the Cambrian conglo- 
merates which rest immediately on any portion of the series are 
almost invariably made up of masses of the rocks below, cemented 
by gritiy materials on an unaltered matrix, and from which the 

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158 Intelligence and Mxecetlaneous Articles. 

pebbles may be easily removed. The great oonglomerates at the 
base of the Cambrians, everywhere in Wales, indicate that there 
were beach- and shallow-water conditions over those areas at the time, 
and that the sea was then encroaching on an uneven land, becoming 
gradually depressed to receive the subsequent Cambrian sediment. 

XX III. Intelligence and Miscellaneous Articles. 

THREE EXPERIMENTS WITH TELEPHONES. 
BY PROFESSOR E. SACHER. 

TN order to ascertain what were the feeblest induced currents in 
-'- the telephone that would be sufficient to produce in the ear di- 
stinct sensations of sound, on December 27, 1877, 1 made the fol- 
lowing experiments. 

1. I lea the closed current-circuit of the telephone, at 20 metres 
distance, parallel with the wire, well insulated with linen and wax, 
of an ordinarv telegraph-apparatus. The signals were given at first 
by six, and afterwards by three Smee's elements (^xr^®^*)^ *^^ 
they were, through the induced currents in the telephone, so dis- 
tinctly audible that the message (by the two signals, long and 
short) could be understood. 

2. I effected a division of the current by uncovering two places 
in the insulated wire distant from each other 20 metres, and fixing 
there the ends of a telephone- wire of equal strength and 120 metres 
long. Beckoning, in addition, the thin wires in the interior of the 
telephone, certainly only a small portion of the current went 
through it ; and yet the rap was perceived with sufficient distinct- 
ness for the message this time also to be understood. (Hence it is 
easy to tap the messages of any open telegraph-line if one can learn 
to read the Morse alphabet by hearing.) 

Experiment 1 succeeds also when the telegraph-wire is connected 
with the thick, and the telephone-wire with the thin wire of a 
Buhmkorff. If we wish to perceive the signals more distinctly, it 
is advantageous to appropriate two telephones to the hearing ; it is 
then, moreover, better to close the other ear against external noises. 

3. I connected the telephone-wire, about 40 metres long, with 
the inner, thick wire of an ordiaary induction-coil, and the wire, 
120 metres in length, of a second telephone-system, with the outer 
thin wire. To my great surprise, we could correspond both from 
the first to the second telephone, and also (indeed apparently still 
better) in the reverse direction, nearly as well as with the connexion 
direct. The words were heard still more distinctly when I inserted 
in the same manner two induction-coils. On the contrary, the ex- 
periment was a failure when a Buhmkorff was employed in this 
way ; the sound was too faint. — Kaiserliche AJcademie der Wisstn^ 
schaften »n TTien, math.-naturw. Classe, January 3, 1878. 



ON THE LIQUEFACTION OP HYDROGEN. BY RAOUL PICTBT. 
(m A LETTER TO M. DUMAS.) 

Geneva, Jan. 11, 1878. 
I have the satisfaction of communicating to you the result of an 
experiment made ou Thursday, January lOth, consisting in the 



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Intelligence and Miscellaneous Articles^ 159 

liquefaction and solidification of hydrogen. I made use of exactly 
the same apparatus as for the liquefaction of oxygen, employing 
protoxide of nitrogen instead of carbonic acid. 

To obtain the hydrogen under pressure, I employed the decom- 
position of formiate of potass by caustic potass. The hydrogen 
was liberated without any trace of water, and the residue is not 
volatile — two conditions essential for the rigorous accuracy of the 
observations. The temperature of the reaction is well defined, and 
did not rise. The liberation of hydrogen proceeded with perfect 
regularity. The pressure reached 650 atmospheres before becoming 
stationary. The hydrogen disengaged corresponded to 252 litres 
at zero. The cold was about — 140^ (I have not yet effected the 
reduction of the measurement of the temperature). When I opened 
the stopcock, liquid hydrogen issued with vehemence from the 
orifice, producing a sharp hissing sound. The jet had a steel-blue 
colour, and was perfectly opaque for a length of about 12 centi- 
metres. At the same time a rattling was heard upon the floor like 
the noise made by hail falling upon the ground, and the hissing was 
changed into a whistling which resembled that heard when a piece 
of sodium is thrown upon water. Almost immediately, the jet 
became intermittent, and shocks were felt in the cock at each issue. 

During the first stream the pressure fell from 650 atmospheres 
to 370. After closing the cock the pressure diminished gradually 
during several minutes down to 215 atmospheres ; it then rose 
again slowly up to 225, at which it again became stationary. I re- 
opened the cock ; but the jet issued in such an intermittent manner 
that it was evident hydrogen had congealed in the tube. This hy- 
pothesis was demonstrated by the progressive exit of all the hydro- 
gen when I had stopped the pumps and the production of cold. I 
explain the difference between these results and those which I 
obtained for oxygen as follows : — 

The atomic weight of hydrogen is ^^ of that of oxygen ; therefore 
the latent heat of liquid hydrogen must be certainly ten times that 
of oxygen. As soon as theexit-cock is opened a portion of the 
liquid stored in the tube evaporates, absorbing such an amount of 
heat by this change of state that the rest solidifies in the tube, even 
before it can be driven out. 

During more than a quarter of an hour we had successive dis- 
charges of hydrogen through the orifice. The fog produced by the 
sudden expansion of the gas at the commencement of the experiment 
descended as far as the ground ; but it ceased completely as soon oa 
the jet became intermittent, which corresponded to the congelation 
of hydrogen in the interior of the tube. It is impossible to con- 
found the vesicular fog of the gas with the appearance of the liquid 
jet at the outset. These different appearances are perfectly dis- 
tinct and give rise to no ambiguity. 

I know the volume of the residue, which is only carbonate of 
potass ; and I shall be able in the next experiment to determine 
the density of liquid hydrogen. — Catn^ptes Rendus de VAeademU des 
Sciences, Jan. 14, 1878, tome Ixxzvi. pp. 106, 107. 



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160 Intelligence and JUtscellaneatu Articles. 

OH THE KLECTBICAL AFTEBCUBBENTS OF TRANSVBRSELT 
MAGNETIZED IBON BODS. BY PBOF. H. BTBEINTZ. 

The experiments leferred to in this ^aper were carried out by the 
Mithor in conjunction with Dr. F. Streints. 

The phenomenon was discovered by Yillari, that in a rod of iron 
or steel throu^ which a galyanic current has passed, when agitated 
after the interruption of this current, a galvanic current is again 
generated the same in direction as that originaUy conducted through 
the rod. He subsequently investigated some properties of these 
aftercurrents, and gave an explanation of the phenomenon : — ^namely, 
that the rod is transversely magnetized by the current ; and if we 
employ the notion of molecular magnets, these arrange themselves 
in concentric circles around the axis of the rod. Now, if the rod 
be agitated after the interruption of the current, the molecular 
magnets obey the direction-force which tends to mingle them again 
irr^ularly. We can here avail ourselves of the representation of 
the molecular magnets returning to the positions which they had 
before the action of the current. Now, in this return they generate 
in the rod an induction-current, to which Yillari gives the name of 
*' agitation-current,'' but which may with equal suitableness be 
designated as an aftercurrent. 

Afterwards H. Herwig studied the properties of transverse mag- 
netism on iron tubes. 

The author now shows that in a very simple manner the quantity 
of the magnetizing force can be calculated which is exerted upon 
the molecidar magnets by the current originally conducted through 
the rod. Starting from Biot and Savart's theorem, that a recti- 
lineal current of infinite length acts upon a pole of a magnet with 
a force inversely proportional to the perpendicular distance of the 
pole from the conductor, the problem is reduced to one of the 
phme ; so that we have to calculate the action of a circular surface 
with uniform mass (the rods investigated had a circular cross sec- 
tion) upon a mass-point situated in the surface. 

In accordance with the laws of force previously stated, however, 
a circular line with uniform mass exerts no action on a point 
situated in the enclosed surface, while it acts on an external point in 
the same plane as if the mass of the circle were coUected in the centre. 

Now by this the calculation becomes very simple, and we obtain, 
as the force which is exerted upon a magnetic pole situated at the 

distance r from the axis,pss^, in which A: is a constant, and a the 

semidiameter of the rod. The total moment upon all the molecular 
magnets contained in the rod is then Es:K2a, where K, again, is 
a constant, and I denotes the length of the rod. 

The author has also investigated by experiment the properties of 
the aftercurrents ; and in so doing he found some conmrmed which 
could be foreseen from the theoretical developments, and also dis- 
covered various other properties, some of them indeed very striking, 
which could not have been determined d priori, — Kaiurliche Aka^- 
demiederWissemchaftm m Wien,fnath»^naturw. CUuHj Dec. 13, 1877. 



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THE 
LONDON, EDINBURGH, akd DUBLIN 

PHILOSOPHICAL MAGAZINE 

AND 

JOURNAL OF SCIENCE. 



/ • ■ • 
* ' - I > 



[FIFTH SERIES.] , . . ^. 



MARCH 1878. 



I 



XXIV. On Reflection of Polarized lAnhtfrom live Equatorial 
Surface of a Magnet, By John Kerb^ LL,D.^ Mathema" 
ticai Lecturer of the Free- Church Training College j Glasgow* 

N trying to cany forward the magneto-optic inquiry which 
formed the subject of my last communication to this 
Magazine t, I proceeded to examine a kteral face of an in- 
tensely magnetized iron bar as a reflector, and had the pleasure 
of obtaining good effects in the first trial. I have lately 

r^rformed a series of careful experiments on the subject ; and 
propose to give an account of these and of their very inter- 
esting results in the present paper. I mean to describe the 
experiments at sufficient length, for the guidance of any one 
who would like to repeat them. Most of them are, I think, 
rather easier and more satisfactory than those described in my 
former paper. 

1. Apparatus. — ^The electromagnet is the same upright horse- 
shoe that was used in my former experiments, a small but 
effective instrument constructed by Mr. Ladd. Each coil 
contains about 200 turns of thick double wire. The coils are 
put into circuit, through a good RuhmkorflTs commutator, 
with a series of six Grove's elements, the connexions being 
made in the usual way as for magnetization of the horseshoe. 

The reflecting bar is a rectangular prism of soft iron, 7 
inches long, 2 wide, f thick. The iron was selected and 
specially forged ; and its structure is homogeneous and very 

* Communicated by the Author. 

t ** On Rotation of the Plane of Polarization by Eeflection from the Pole 
of a Magnet," May, 1877. 

FhU. Mag. S. 5. Vol. 5. No. 30. March 1878. M 



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162 Dr. J. Kerr on Reflection of Polarized Light 

fine. One lateral face of the bar (7 by f ) was planed and 
careftilly polished by a skilled workman. 

It may be worth mentioning that three such bars were 
forged at the same time, were cemented together, planed and 

Eolished in block, and then separated. The middle one was 
ept as the best reflector ; but most of my results were ve- 
rified upon each of the three. 

2. Arrangements. — ^The electromagnet stands upright upon 
a solid table ; the reflecting bar lies flat and stably on the 
poles of the horseshoe, in the position of an armature, its 
length horizontal, and its polished face vertical ; the two 
Nicols and the lamp stand upon the same table as the magnet, 
and at the same height as the mirror. The diagram shows all 
the pieces, in horizontal section through the lamp L and the 




observer's eye E. N is the first Nicol, C the point of incidence 
on the reflector AB, and N' the second Nicol. The poles of 
the horse-shoe, below the bar, are indicated by the dotted 
circles. The piece P between the lamp and the first Nicol was 
often found useful in the more delicate observations : it is a 
metallic screen, containing a long horizontal slit about J of an 
inch wide. Sometimes the flat flame L has its edge presented 
to C ; and then, the piece P being in position, the object seen 
at through N' is a small segment of the flame, sensiblv 
square. But generally, except when the angle of incidence is 
near 90^, the width of the flame is presented ; and then the 
object seen in the mirror is a long horizontal rectangle, uni- 
formly illuminated, strongly outlined above and below, and 
bringing out small changes of small intensity very delicately. 

In the diagram, the axis of the bar A B is produced through 
the end B next the observer ; the extremity JF of the axis thus 
produced is used afterwards as a point of reference. 

In all my later observations, the values of the angle of in- 
cidence i L C E were assigned beforehand as carefully as 
possible, but by a method which cannot pretend to great 
accuracy. A broad sheet of drawing-paper, which had oeen 
cut away at the proper angle through one of its comers, was 
laid flat on the table, and aligned against the fixed stand of 



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from the Equ<itorial Surface of a Magnet. 163 

the magnet and the movable stand of the lamp, each of the 
stands presenting suitably a long straight edge in contact with 
ilie table. 

It will be observed that, according to these arrangements, 
the lines of magnetic force at the point of incidence remain 
sensibly parallel to the trace of the plane of incidence on the 
reflecting surface, through all changes of incidence from near 
grazing to near normal. 

3. Specification of Rotations of the Nicoh. — I shall have 
occasion repeatedly to speak of right-handed and left-handed 
rotations of the two Niools. In the employment of these 
terms, I shall always view the second Nicol from the point E, 
and the first Nicol from the point C. By a right-handed ro- 
tation of the second Nicol, I mean, therefore, a rotation of the 
analyzer which is with watch-hands when viewed from E ; 
and by a left-handed rotation of the first Nicol, I mean a rota- 
tion of the polarizer which is against watch-hands when viewed 
from the point of incidence C. 

4. Specifcation of Magnetizations of the Reflector. — -In the 
statement of results, I shall always specify the two magnetiza- 
tions of the reflector by giving the direction of the magnetizing 
current, the current being supposed to circulate spirally round 
the bar A B, out of one coil into the other. These directions 
of magnetizing currents may of course be conceived and re- 
membered more simply, as the directions of Amperean currents 
in the maoietized bar. By a right-handed current I shall 
always understand here, a magnetizing current whose effective 
direction, round the reflecting bar A B, is with watch-hands 
when viewed from the point F. 

The three points of reference now fixed will be carefully 
adhered to: — E for movements of the second Nicol or analyzer ; 
C for movements of the first Nicol or polarizer ; and F for 
directions of the magnetizing current, or for directions of Am- 
perean currents in the magnetized reflector. 

5. Optical Observations with the Mirror and the two Nicols. — 
These belong properly to Optics, and present nothing new ; 
some of them, also, were described in my former paper ; but 
thev are given here for their bearing on subsequent methods 
and results, and for the useful practice which they afford in 
the management of the apparatus. Suppose the pieces placed 
aB in the diagram (2). 

Whatever be the angle of incidence, there are only two ar- 
rangements of the Nicols which give pure extinction of the 
reflected image. In one of these arrangements the principal 
section of the first Nicol is parallel to the plane of incidence; 
and in the other it is perpendictdar. 

M2 



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164 Dr, J, Kerr on Reflection of Polarized Light 

When the incidence is between grazing and principal^ 90*^ 
to 85°, and the two Nicola are initially at pure extinction, any 
very small rotation of the first Nicol may be neutralized per- 
fecfly, or very nearly, in the polariscope, by a small rotation 
of the second Nicol, provided the two rotations are both righi- 
handed or both left-handed, and properly related to each other 
in magnitude ; but if the two rotations are one right-handed 
and the other left-handed, the effect of one in the polariscope 
is strengthened by the other ab initio. 

When the incidence is between principal and normal, 65° 
to 30°, and the two Nicols are initially at pure extinction, any- 
very small rotation of the first Nicol mav be similarly neutrar- 
lized by a small rotation of the secona Nicol, provided the 
rotations are one right-handed and the other left-handed ; but 
if the rotations are both right-handed or both left-handed, the 
effect of one is strengthened by the other ab initio. 

When the incidence is about 75°, and the two Nicols are 
initially at pure extinction, no small rotation of the first Nicol 
can be neutralized, or its effect in the polariscope sensibly 
weakened, by a rotation of the second Nicol either way. 

It appears from these observations, that the arrangement 
of the two Nicols for extinction is very sharply defined at or 
very near the principal incidence only. At other incidences 
there is a sensible though small range of angular magnitude, 

increasing as ihe angle of incidence approaches either ^ or 0, 

through which we can turn the first Nicol either way from pure 
extinction, without losing the power to recover a pretty good 
extinction by a proper displacement of the second Nicol. 

The next observation requires a compensating slip of glass. 
That which I generally employ is a piece of good plate, ^ of 
an inch thick, 1 wide, and 7 or 8 long. It is held between the 
mirror and the second Nicol, its plate-faces perpendicular to 
the reflected ray, and its length at 45° to the plane of reflection. 
If the slip has been properly chosen, and is in good condition, 
it is quite inactive in the polariscope, except when purposely 
strained by the obser\'er's hands. The only strains applied 
are compression along the length and tension along the 
length. 

When the angle of incidence is about 75°, and the two 
Nicols are initially at pure extinction, any very small rotation 
of the first Nicol is neutralized perfectly or very nearly by the 
compensating slip feebly strained : the right-handed rotation 
is neutralized by compression right hand down, and, therefore, 
also by tension left hand down : and the left-handed rotation 
is neutralized by tension right hand down, and, therefore, also 



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from the Equatorial Surface of a Magnet. 165 

by compression left hand down. By a contrary strain with 
the same hand down in each of these cases, or by a similar 
strain with the other hand down, the effect of rotation of the 
first Nicol in the polariscope is very clearly strengthened ab 
initio. These observations with the slip of strained glass were 
described and explained in my former paper. It may be re- 
membered that a right-handed rotation of the first Nicol was 
there compensated by tension right hand down, and not, as 
here, by compression right hand down. The reason of this 
difference is obvious, the plane of reflection being there vertical, 
but here horizontal. I proceed now to the observations with 
the ms^netized mirror and the two Nicols, placed always as 
in the oiagram (2). 

6. First Experiment. — The plane of polarization of the 
light incident upon the mirror is constantly parallel to the 
plane of incidence ; and the initial extinction is made as pure as 
possible. 

(1) The second Nicol is turned righthandedly through an 
extremely smaJl angle from the position of extinction ; and the 
light thus restored faintly in the polariscope is watched for 
changes of intensity when the reflecting bar is magnetized suc- 
cessively by contrary currents. 

(2) The second Nicol is turned lefthandedly through an 
extremely small angle past the position of extinction ; and the 
optical effects of contrary magnetizing currents are observed 
as in the former case. The following is an accurate statement 
of the results : — 

(1) The light restored from extinction by a very small 
right-handed displacement of the second Nicol is always 
strengthened by a right-handed magnetizing current, and 
always weakened by a left-handed current. 

(2) The light restored from extinction by a very small left- 
handed displacement of the second Nicol is always weakened 
hj a right-nanded current, and always strengthened by a left- 
handed current. 

I The intensiiy of these optical effects of magnetization varies 

/ very noticeably with the angle of incidence. About incidence 

/ 85° the effects are very faint, but perfectly regular and much 

better thaix merely sensible ; about incidence 75° they are 

more distinct, and very sensibly stronger ; about incidences 

65° and 60° they are comparatively clear and strong, a good 

deal stronger than at 75° ; about incidence 45° they are still 

pretty strong, but very sensibly fainter than at 60° ; about 

incidence 30 they are again very faint, much the same as at 85°. 

Between 30° and the normal I have made very few obser- 

TationS; and these not satisfactory ; between 85° and 90° I 



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166 Dr. J. Kerr on Reflection of Polarized Light 

have obtained no snre eflfect, nothing that could be recovered 
with certain^ ; but within the preceding range of incidence. 
85^ to 30^, I have always recovered the elects easilji ana 
always in the forms now stated. 

The right-handed current conspires with (or strengthens £he 
efiFect of) a right-handed rotation of the second Nicol, and so 
forward consistently, the optical effect of the current being 
reversed by reversal of the current, and also by reversal of ro- 
tation of the second Nicol. 

7. Returning for a moment to the method of observation, 
suppose the second Nicol turned righthandedly through a 
small angle from extinction. 

(1) Only right-handed currents are applied, the circuit 
being closed and broken at intervals. When the circuit is 
closed, the li^ht is strengthened in the polariscope ; when the 
circuit is broten, the lignt is weakened. 

(2) Only left-handed currents are applied. When the 
circuit is closed, the light is weakened ; when the circuit is 
broken, the light is strengthened. 

(3) Contrary currents are transmitted in succession, the 
reversal being made by a rapid half-turn of the commutator. 
In this case, the passage from left-handed current to right- 
handed strengthens the light in the polariscope, and the con- 
trary passage from right-handed current to left-handed weakens 
the light. 

The magnetic changes of the bar in (3) are more than twice 
as great as those in (l) or (2), because of the imperfect de- 
magnetization of the bar at the instant of break. It is observed 
accordingly in the experiment, that the optical changes in (3) 
are far superior to those in (1) and (2), generally much more 
than twice as strong. Sometimes, indeed, about the extreme 
incidence 85^ or 30°, and when circumstances are unfavour- 
able, I find the effects in (3) still quite distinct, while those in 
(1) and (2) are almost or altogether imperceptible. Another 
fact of the same kind which i have noticed in (1) and (2) is, 
that the effect of make^ whether it be an increase or a diminu- 
tion of intensity in the polariscope, is generally more distinct, 
strikes the eye more sharply, than the effect of break. I may 
state here finally that, when the effects are very weak, the 
observer may often bring them out better and better by making 
the rotation of the second Nicol smaller and smaller till the 
restoration in the polariscope is merely an imperfect extinction. 

8. Second Experiment, — The plane of polarization of the 
light incident on the mirror is constantly perpendicular to the 
pkne of incidence. All the other arrangements, and the 
observations^ are precisely as in the first experiment. The 



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frcm the Equatorial Surface of a Magnet. 167 

seoond Nicol is turned through an extremely small angle from 
the position of extinction^ first righthandedly^ then left- 
handedlj; and in each case the effects of the two magnetizing 
currents are observed in the polariscope. 

About incidence 85^^ the light restored by a right-handed 
rotation of the second Nicol is strengthened by a right-handed 
current^ and so forward, the effects being undistinguishable in 
any way from those obtained in the first experiment at the 
same incidence, except that (under equally favourable con- 
ditions) they are certainly and considerably fainter. About 
incidence 80^ the effects are still of the same kind, but a good 
deal fainter — so faint, indeed, that they cannot be brought out 
Tcry distinctlv except under the most favourable conditions 
(the battery iresh, the initial extinction very pure, and the dis- 
placement of the second Nicol extremely small). About inci- 
dence 75^ the regular effects disappear. About incidence 70^ 
they reappear very faintly, as faintly as at 80°, but quite dis- 
tinctly contrary to those obtained at 80° and 85°: the light 
restored by a right-handed rotation of the second Nicol is now 
weakened by a right-handed current, and strengthened by a 
leffc-handed current, and so forward. At incidences 65°, 60°, 
45°, 30°, the effects are of the same kind as at 70°, still con- 
traiy, therefore, to those obtained at 85° ; about incidence 60° 
they are comparatively clear and strong, though sensibly fainter 
than those obtained in the first experiment at the same inci- 
dence ; about 30° they are faint but still distinct, and clearly 
stronger than the contrary effects obtained at 85°. It appears 
thus that, in the second experiment, the optical effects of 
magnetization fall under two distinct cases : — 

(1) Between grazing and principal incidences, the law is 
the same as in the first experiment : the right-handed current 
conspires virith a right-handed rotation of the second Nicol, and 
so forward. 

(2) Between principal and normal incidences, this law is 
simply reversed : the left-handed current conspires with a 
right-handed rotation of the second Nicol, and so forward. 

9. Any details that could be given as to the methods of ob- 
servation in tiie second experiment would be a virtual repetition 
of article (7) ; but some remarks are due to the case of prin- 
cipal incidence. In my earlier observations at and about- 
incidence 75° in this experiment, I was much perplexed with 
the results. The effects of magnetization were sometimes im- 
perceptible, while in other cases they were quite sensible 
though faint. Sometimes they were similar to the effects at 
85°, and sometimes similar to the contrary effects at 60^; but 
they were more frequently of another kind : either the right-^ 



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168 Dr. J. Kerr on Reflection of Polarized Light 

handed current or the left-handed^ sometimes one and some- 
times the other, conspired feebly with each rotation of the 
second Nicol, the right-handed and the left-handed in succession. 
The latter effects were certainly due to slight misplacements of 
the first Nicol, which impairea the purity of the initial extinc- 
tion. All these irregularities disappeared in the most carefullj 
conducted of my later obseryations, where due attention was 
giyen to two principal conditions — ^the assignment of a proper 
yalue (75° exactly or nearly) to the angle of incidence, and 
the purification of the initisd extinction oy exact adjustment 
of the first Nicol. Upon the whole, the result of my obserya- 
tions is that, in the second experiment, at and about incidence 
75^, neither magnetization has any regular effect in the pola- 
riscope. I haye little doubt that, with higher powers, magne- 
tization would haye a distinct optical effect, and that effect an 
increase of intensiiy in eyery case ; but I merely describe 
things at present as I haye seen them. 

10. Third Experiment.— The two Nicols are placed initially 
at pure extinction, the plane of polarization of the light inci- 
dent on the mirror being parallel to the plane of incidence. 
The second Nicol remains nxed. 

The first Nicol is turned through an extremely small angle 
from the position of extinction, first righthandedly and then 
lefthandedly ; and in each case the effects of the two magne- 
tizing currents are obseryed in the polariscope. 

About incidence 85° the light restored by a right-handed 
rotation of the first Nicol is weakened by a right-handed cur- 
rent, and strengthened by a left-handed current; while the 
light restored by a left-handed rotation of the first Nicol is 
strengthened by a ri^t-handed current, and weakened by a 
left-handed current. The effects are fainter than those obtained 
at the same incidence in the first experiment, but they are 
distinct and perfectly regular. About incidence 80° the 
effects are still regular and of the same kind, but yery faint, 
and requiring extremely small displacements of the first Nicol 
to bring them out clearly. About incidence 75° the regular 
effects disappear ; and some irregular effects, which make their 
appearance here as in the second experiment, are eliminated 
by the assignment of a proper yalue to the angle of incidence, 
and by exact adjustment of the second Nicol. 

At incidences 65°, 60°, 45°, 30°, the effects are contrary to 
those obtained at 85° : the light restored by a right-handed 
rotation of the first Nicol from extinction is strengthened by 
a right-banded cun-ent, and so forward. At incidence 60 , 
und eyen at 45°, the effects are yery distinct and comparatiyely 
strong; but always fainter than those obtained at the same in« 



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frcm the Equatorial Surface of a Magnet. 169 

cidences in the first experiment. It appears thus that in the 
third experiment, as in the second, the optical effects of mag- 
netization fall nnder two cases : — 

(1) Between grazing and principal incidences the right- 
handed current conspires with a left-handed rotation of the 
first Nicol, and so forward consistently. 

(2) Between principal and normal incidences, the preceding 
law is simply reversed ; the right-handed current conspires 
with a right-handed rotation of the first Nicol, and so forward. 

11. Fourth Experiment, — The two Nicols are placed initially 
at pure extinction, the plane of polarization of the light in- 
cident on the mirror being perpendicular to the plane of inci- 
dence. All the other arrangements and the procedure are 
as in the third experiment : me second Nicol remains fixed ; 
and the first Nicol is displaced through a very small angle 
from the position of extinction, first righthandedly and then 
lefthandedly. The results are very similar to those obtained 
in the first experiment 

(1) The light restored by a right-handed rotation of the 
first Nicol is always weakened by a right-handed current, and 
always strengthened by a left-handed current. 

(2) The light restored by a left-handed rotation of the first 
Nicol is always strengthened by a right-handed current, and 
always weakened by a left-handed current. 

Very near grazing incidence, between 90° and 85°, the 
effects are insensible ; about incidence 85° they are very faint, 
but regular and quite distinct ; they inci'ease in strength quite 
evidently through the incidences 80°, 75°, 70°, to somewhere 
between 65° and 60°, where they are, I think, as clear and as 
strong as those obtained in tie first experiment ; they then 
diminish gradually to incidence 30°, where they are very 
faint, but still somewhat stronger than at 85°. 

It appears thus that, in the fourth experiment, the right- 
handed current conspires always with a left-handed rotation of 
the first Nicol. 

12. The four experiments which have been described were 
repeated at several incidences with mirrors of steel. Some 
finely polished knife-blades were tried, and several masses of 
other forms. The best was a small bar-magnet of hard steel, 
which had one of its narrow faces polished on a cutler's wheel 
(one of those large wheels used for sword-blades). The curva- 
ture of this mirror was inconsiderable ; and its polish was ex- 
tremely fine. The arrangements were as in the diagram (2)^ 
the bar being laid stably from pole to pole of the horseshoe. 

All the old effects were recovered regularly. Only one 
thing new attracted my notice, which was, the greater superi- 



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170 Dr. J. Kerr an Reflection of Polarized Light 

oriiy of reversal to breakj and even of nuike to Ireak^ in the 
case of steel, than in the case of soft iron (7) ; bat I do not 
know how far mj judgment in this matter may have been in^* 
flaenced bj expectation. 

13. St/nopsis of the preceding JResuUe-^^-ttoo Lowe with two 
Exceptions. 

First Law. The right*handed carrent conspires with a small 
right-handed rotation of the analyzer from extinction ; and so 
forward. 

Second Law. The right-handed carrent conspires with a 
small left handed rotation of the polarizer from extinction ; and 
so forward. 

First Exception. When the plane of polarization of the light 
incident on tiie mirror is perpendicalar to the plane of inci- 
dence, the First Law is reversed for all incidences between 
principal and normal. 

Second Exception. When the plane of polarization of the 
light incident on the mirror is parallel to the plane of incidence, 
the Second Law is reversed for all incidences oetween principal 
and normal. 

14. I may say here, with reference to the various statements 
of fact which I nave made in the preceding articles, that they 
are founded on a large number of perfectiy concordant obser* 
vations. The angles of incidence quoted are of course only 
rough approximations (2); and some of the other details may 
be modified by future observation ; but the broad fects are as 
certain to my mind as any thing in Physics. 

The next two experiments afford interesting verifications of 
former results, as they show that when two actions already 
known as conspiring actions are applied separately, their 
optical effects are similar, or ratiier similarly directed. To 
prepare the way, I must mention some delicate optical phe- 
nomena, which present themselves in connexion with very 
small movements of either Nicol through the position of ex- 
tinction. Each Nicol is supposed to be near the mirror ; 
the piece P is in position (2); and the incidence is between 
principal and noimal. When the extinction is perfect, and the 
observer's attention has been once directed, he can generally 
detect an obscure cloud, which is pretty definitely formed, and 
sometimes finely formed as a dark horizontal band, covering 
the old place of the reflected image, and extending well across 
the field. In these circumstances, any almost immeasurably 
small rotation of either Nicol, in one direction or the contrary, 
produces a regular and very sensible change in the field of 
vision — a contmuous displacement of the band, upwards in one 
case and downwards in the other, the form and direction of 



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from the Equatorial Surface of a Magnet. 171 

the band being fairly preserved through large displacements. 
In the next two experiments^ I make use of this movement of 
the band as a mere initiation of restoration from pure extinction 
in the polariscope. I call it a mere initiation of restoration, 
because the band has already undergone a lar^e displacement 
over the surface of the mirror, by rotation of tne second Nicol 
or otherwise, before there is any sensible restoration of the re- 
flected image from pure extinction. 

15. Fifth Experiment. — ^The plane of polarization of the 
light incident on the mirror is parallel to the plane of inci- 
dence; and the extinction in the polariscope is made as pure as 
possible, the old place of the reflected image being covered by 
an obscure cloud or band (art, 14). The observations now to 
be described in this article and in art. 16 have been made re- 
peatedly at the four incidences 70°, 65°, 60°, 45°, with con- 
sistent and uniformly distinct results. 

(1) The two Nicols are untouched, and remain in ilieir 
initial positions of pure extinction. A left-handed current 
sends the band up through a small distance very clearly ; a 
right-handed current sends the band down ; contrary currents 
in rapid succession act accordingly, and give larger displace- 
ments of the band ^art 7). 

(2) With open circuit, a right-handed rotation of the second 
Kicol through the position of extinction sends the band down 
very clearly. Compared with observation (1), this verifies the 
First Law stated in art. 13, that the right-handed current con- 
spires with a right-handed rotation of the second Nicol. 

(3^ With open circuit, a right-handed rotation of the first 
Nicol through the position of extinction sends the band down 
certainly, though the efiect is not generally so good as that in 
(2). The resSts in (1) and (3) verify the exception to the 
second Law stated in art. 13, as the present incidences lie be- 
tween principal and normal. 

16. Sixth Experiment. — The plane of polarization of the 
light incident on the mirror is perpendicular to the plane of 
incidence ; other things as in art. 15. 

(1) The efiects of magnetization obtained in art. 15 are 
simply reversed. A right>-handed current sends the band up 
very clearly ; a left-handed cuiTent sends the band down; con- 
trary currents in rapid succession act accordingly. 

(2) With open circuit, a right-handed rotation of the second 
Nicol sends the band down (exactly as in art. 15). This agrees 
with the exception to the First Law stated in art. 13. 

(3) With open circuit, a right-handed rotation of the first 
Nicol sends the band down (exactly as in art. 15). This agrees 
with the Second Law (art. 13). 



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172 Dr. J. Kerr an Reflection of Polarized Light 

The reader would have a false view of these two experi- 
ments, if he thought there was an^ thing uncertain about the 
phenomena, any mere guess-work m the observations. On the 
contrary, the eflFects are perfectly regular, almost invariably- 
very sensible, and sometimes beautifully distinct. In one or 
two trials which I conducted in favourable circumstances alon^ 
with several friends, I found that the movements of the band, 
whether produced by currents or by displacements of the 
second Kicol, were suflScient to make a strong, correct, and 
immediate impression upon an eye quite uneducated, and 
which had been merely du^cted to the right point. 

I think that any discussion of the optical phenomena here 
utilized would be quite irrelevant. 

17. In the next two experiments, I apply the compensating 
slip of glass already described (art. 5). It is introduced into the 
path of the reflected light, between the mirror and the second 
Nicol, its length at 45^ to the plane of reflection, and its plate- 
faces perpendicular to the ray. Of the four methods of strain- 
ing the glass, I generally choose compression right hand down. 
To apply the action, I hold the slip at the lower end, between 
finger and thumb of the right hand, taking care to have the 
piece properly directed, and exert a small pressure downwards 
by the fore-finger of the left hand laid along the upper end of 
the slip. A very feeble pressure is suificient to give a 
perceptible restoration of the reflected image from pure 
extinction. 

18. Seventh Experiment. — The plane of polarization of the 
light incident on the mirror is parallel to the plane of incidence ; 
and the two Nicols are kept at pure extinction. 

When the light is restored very faintly by the compressed 
glass, it is not sensibly strengthened or weakened by either 
magnetization of the mirror ; and this holds true for all inci- 
dences between 85° and 30°. Sometimes, indeed, when 
working in this way, I obtained sure though very faint changes 
of intensity in the polariscope — an increase by one current, and 
a decrease by the otiier ; but in several cases where these effects 
were closely examined, they were found to be caused by imper- 
fection of initial extinction, and particularly by slight mis- 
placements of the second Nicol. Upon the whole, if there 
was any regular effect here, it was too faint to be certainly 
characterized. 

19. Eighth Experiment. — The plane of polarization of the 
light incident on the mirror is perpendicular to the plane of 
incidence ; and the initial extinction is made as pure as possible, 
particular attention being given to the placing of the first 
^icol. Other things are as in the seventh expenmenti 



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from the Equatorial Surface of a Moffnet. 173 

About incidence 75°, the light restored by compression right 
hand down is strengthened by the right-handed current, and 
weakened by the left>>handed current, the actions of the currents 
from reversal being regular and very clear though faint. 

About incidence 60^ the efFects are of the same kind, but a 
creat deal stronger. Each of the currents acts clearly now 
from its own break (art. 7), the right-handed current conspiring 
always with compression right hand down, therefore also with 
tension left hand down ; and the left-handed current conspiring 
always with tension right hand down, therefore also with 
compression left hand down. These four cases of conspiring 
actions, as well as the four corresponding cases of contrary or 
mutually compensating actions (right-handed current with 
tension right hand down, &c), are all brought out regularly 
and strongly about incidence 60°, 

At incidence 45° the effects are still of the same kind, regular 
and Tery distinct though not strong, not nearly so strong as 
at 60°. Between principal incidence and grazing, about 85°, 
the effects are still of the same kind, the right-handed current 
clearly conspiring here as elsewhere, though here very faintly, 
with compression right hand down. 

20. It is worth noticing that we might have anticipated some 
of the results brought out in the last two experiments, those 
of them, namely, that are obtained at incidences near 75°. It 
has been mentioned already as a result easily obtained with 
the present apparatus, that a small right-handed rotation of the 
first Jtficol from extinction, at or near incidence 75°, is neutra- 
lized by compression right hand down (art. 5). From this we 
infer that compression right hand down is optically equivalent, 
at least in an approximate manner, to a left-handed rotation 
of the first Nicol, We have, then, two cases, according to the 
fourth and third experiments : — 

(1) When the plane of polarization of the light incident on 
the mirror is perpendicular to the plane of incidence, the right* 
handed current conspires with a left-handed rotation of the 
first Nicol, and should conspire therefore with the optical 
equivalent of that rotation, compression right hand down, as 
it does actually in the eighth experiment. 

(2) When the plane of polarization is parallel to the plane of 
incidence, and the angle of incidence is about 75°, neither 
current conspires with any small rotation of the first Nicol ; so 
that neither current should conspire with compression right 
hand down, which is actually the case in the seventh ex- 
periment*. 

21. I have now given all my positive results ; but there are 



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174 Dr. J. Kerr on Reflection of Polarized Light 

two oilier lines of experiment which I have tried without effect^ 
and which ought to oe briefly noticed. 

(1) The mirror^ aB formerly, an equatorial face of a magne- 
tized bar^ the plane of incidence perpendicular to the lines of 
magnetic force, and the incidence varying from near normal 
to near grazing. The arrangements were of course somewhat 
different from mose ah*eady described ; but they were not more 
diflScult^ and were made witli equal care; and I think that the 
experiments were altogether as delicate as any of the preceding. 
Working in this way at different times, I saw no appearance 
of optical effect of magnetization. 

(2) The mirror an equatorial face of a magnet, the incidence 
normal, and the inclination of the plane of incidence to the 
lines of magnetic force varying from 0° to 90°. As the normal 
incidence was obtained by the employment of a mirror of un- 
ailvered glass, the light was a good deal weaker than formerlv ; 
but otherwise the experiment was as delicate as any of tne 
preceding. Nothing hke an optical effect of magnetization 
was observed in any instance. 

From these experiments, and from all that I have seen upon 
the subject, I think it probable, in the highest degree, that 
magnetization of a reflector even to saturation would be abso- 
lutely without optical effect in the cases now exemplifled (that 
is, in the case of normal incidence upon an equatorial face), and 
in any case where the fronts of the incident and reflected waves 
are parallel to the lines of magnetic force. 

I return now to the consideration of our first arrangement, 
where the lines of magnetic force are parallel to the intersection 
of the reflecting surface and the plane of incidence. 

22. Law of the optical action of magnetism at incidences 
ne ar g razing. 

Whatever be the angle of incidence between grazicg and 
principal, the effect of magnetization of the mirror, when sen- 
sible, is to turn the plane of polarization of the reflected light 
through a very small angle, in a direction always contraiy to 
that of the Amperean currents ; for, whatever be the angle of 
incidence between grazing and principal, the two laws stated 
in art. 13 hold true mrougnout the first four experiments with- 
out exception. 

(1) The right-handed current conspires with a right-handed 
rotation of the second Nicol. But the effect of a righi-handed 
rotation of the second Nicol (before magnetization of the 
mirror) is virtually to turn the reflected ray lefthandedly, or 
to displace its plane of polarization lefthandedly, with reference 
to the principal section of the analyzer. And' since the right- 
handed current conspires with the right-handed rotation of the 



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from the Equatorial Sur/aoe of a Magnet, 175 

analyzer, it addfi actually to the yirtnal l6f)>-banded rotation 
of the reflected ray, or turns the plane of polarization left- 
handedlj. 

(2) The right-handed current conspires with a left-handed 
rotation of the first NicoL But we have seen in art. 5, that a 
left>-handed rotation of the first Nicol is neutralized (near 
grazing incidence) by a left-handed rotation of the second 
Sficol ; and from this we infer that a left-handed rotation of 
the first Nicol turns the plane of polarization of the reflected 
ray lefthandedly. And since the right-handed current con- 
epirea with a left-handed rotation of tiie first Nicol, it adds to 
the consequent left-handed rotation of the reflected ray, or turns 
the plane of polarization lefthandedly. 

Of course this proof assumes, and the conclusion implies, 
that the reflected light may be considered as approximately 
plane-polarized in dl the preceding instances of conspiring 
actions, as well as in the corresponmng instances of mutually 
compensating actions, both in the optical observations (art. 5% 
and throughout the first four experiments. 

23. It is proved thus beyoncl question, at least as a very 
approximate expression of mcts, that, near grazing incidence, 
the efiect of magnetization of the mirror upon a reflected ray 
is to turn the plane of polarization through an extremely smaU 
angle, in a direction contrary to that of the Amperean currents. 
Under what conditions, on what assumptions, may this be ac- 
cepted as the law of the action at all incidences ? To prepare 
for a definite answer to this question, I shall first subject the 
statement of the law to a simple transformation. 

When the vibration reflected from the unmaffnetized mirror 
is either parallel or perpendicular to the plane of reflection, the 
effect of magnetization is to introduce a new and very small 
component vibration in a direction perpendicular to the primi- 
tive vibration, the sense of the new component being that 
assumed by the primitive vibration when turned through a 
right angle in a direction contrary to the Amperean currents. 
And for incidences between grazing and principal, the difier- 
ence of phases of the two components (the primitive and the 

new) is much nearer to than to ^. 

It is important to observe here, that the results obtained in 
the fifth and sixth experimenis necessitate the assumption of 
some such law as this, even for incidences between principal 
and normal. For the direction of the primitive vibration is in 
those experiments exactly parallel or perpendicular to the 
plane of reflection, and the Nicols remain constantly in i;heir 
initial position of pure extinction ; so that the observed effects 



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176 Dr. J. Kerr on Reflection 0/ Polarized Light 

of magnetization, effects which are of the same kind as those 
proda^ by rotation of the second Nicol, cannot be explained 
by any mere changes of the primitive yibration in amplitade 
or phase, or by any thing except the introdaction of a new and 
very sniall component in a direction perpendicular to the 
primitive vibration. 

24. General Law of the Action of Magnetism upon the Re- 
fleeted Ray. 

The three following assumptions appear to me to afford a 
perfect explanation of all the principal phenomena. They 
were suggested as above, and were tested oy a careful mathe- 
matical discussion of the results of all the experiments in suc- 
cession. The discussion presents little difficulty, but is too 
tedious to be offered here. 

(1) When the original vibration is parallel or perpendicular 
to the plane of reflection, the effect of magnetization of the 
mirror is to turn the vibration through a very small angle in a 
direction contrary to the Amperean currents. 

The resolved parts of the vibration so turned, one in the 
direction of the primitive vibration and the other peipendicular 
to it, may be called the primitive component and the new 
component respectively, as in art. 23. 

(2) The primitive component is always reflected according 
to the same laws of retardation of phase, after magnetization 
of the reflector as before. 

(3) Whether the new component be parallel or perpendi- 
cular to the plane of reflection, and whatever be the angle of 
incidence, the phase-retardation of the new component (with 
reference to a standard reflected ray, polarized in the plane of 
incidence, and incident in the same phase as the actual primi- 
tive), is always an angle in the first quadmnt, and much nearer 

to zero than to ■^. 

It will be admitted that the assumption (3) is a very re- 
markable one, and very important if true. I hope to see this 
geometric theory of the phenomena verified by the mathema- 
ticians, or something better put in its place. 

25. It would be superfluous now to offer any explanation of 
the absence of all optical effect of magnetization in the case 
of normal incidence (art. 21). It is not so easy to understand 
the absence of effect at incidences very near grazing, 85° to 
90°, in the first four experiments. We might expect indeed, 
on the contrary, that as the ray approaches parallelism to the 
lines of force, or as the front of the wave approaches perpen- 
dicularity, the magnetic force would act at a greater advan- 
tage, and the optical effect would therefore become stronger. 



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from the Equatorial Surface of a Magnet, 111 

Bat against this we have what appears to be fairly established 
by observation as a general truth in optics, that the specific 
differences of reflectors become less and less marked as inci- 
dence approaches grazing, until at grazing they almost en- 
tirely disappear. 

26. I shall not make any lengthened comparison between 
the effects now observed in connexion with the equatorial sur- 
face and those formerly obtained in the case of the polar sur- 
face. The two sets of results are not inconsistent, nor do they 
differ materially in any way, except that the present set con- 
tains a larger amount of detail as to the variations of optical 
effect, variations extending even to reversal. I have no doubt 
that tiiis enlargement of results is due to better means and 
improved arrangements in the present series of experiments. 
It will be remembered that a submagnet, separated from the 
mirror by a very narrow chink, was found indispensable in 
the case of the polar surface. In the present experiments 
there is no place for such an adjunct, and the reflector is fully 
exposed to view at all incidences, which is a great improve- 
ment. The new arrangements are also simpler and more ma- 
nageable upon the whole, and much better adapted for delicate 
and exact optical observation. 

In one respect I have certainly found the polar surface 
superior to the equatorial. In the case of the polar surface, 
and with the power that I have applied, it is easy to obtain, by 
magnetic force alone, a very distinct restoration of the reflected 
light from pure extinction, though the restoration is never 
very strong ; but in the case of the equatorial surface, and 
with equal or greater powers, I have never seen any stronger 
effect of unassisted magnetic force than those fine movements 
of the band in the fifth and sixth experiments. 

27. The first facts of magneto-optics discovered long ago 
by Faraday, their more immediate consequences discovered 
afterwards by Verdet and others — these and the additional 
facts now published by myself must be all included ultimately 
under one physical theory. It is very probable that the 
remarkable theory of magnetism which has been advanced by 
Sir William Thomson in a discussion of the former class of 
facts, wiU apply as well to the latter. Probably also the theory 
itself may receive additional confirmation in the process. I 
think it equally probable that the new facts will find important 
applications in the mechanical parts of the Wave Theory. But 
in any event there is a new physical action secured thoroughly 
to science, a specific action of magnetized iron upon light in- 
cident at any point of its surface. 

Glasgow, January 21, 1878. 

PhU. Mag. S. 5. VoL 5. No. 30. March 1878. N 

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[ 178 ] 

XXV. Proof of the hitherto undemonstrated Fundamental 
Theorem of Invariants. By J. J. Sylvester, Profeeeor of 
Mathematics at the Johns Hopkins University ^ Baltimore*. 

I AM about to demonstrate a theorem which has been wait- 
ing proof for the last quarter of a century and upwards. 
It is the more necessary that this should be done^ because the 
theorem has been supposed to lead to false conclasions, and its 
correctness has consequently been inipugnedt* But, of the two 
suppositions that might be made to account for the observed 
discrepancy between the supposed consequences of the theorem 
and ascertained facts — one that the theorem is false and the 
reasoning applied to it correct, the other that the theorem is 
true but that an error was committed in drawing certain de- 
ductions from it (to which one might add a tnird, of the 
theorem and the reasoning upon it being both erroneous) — 
the wrong alternative was chosen. An error was committed 
in reasoning out certain supposed consequences of the theorem ; 
but the theorem itself is perfectly true, as I shall show by an 
argument so irrefragable that it must be considered for ever 
hereafter safe from all doubt or cavil. It lies at the basis of 
the investigations begun by Professor Cayley in his * Second 
Memoir on Quantics, which it has fallen to my lot, with no 
small labour and contention of mind, to lead to a happy issue, 

• Communicated by the Author. 

t Thufl in Professor Fai de Bruno's valuable Thiorie des Formes 
Binairesy Turin, 1876, at the foot of page 160 occurs the following pas- 
saffe: — "Oela suppose eesentiellement que les ^nations de condition 
8<nent touUs ftuUpendantes entr'elies, ee qui fC est pas toujours le cos, aind 
^u'il r^sulte des recherches du Frot Gordan sur les nombres das cora- 
nants des formes quintique et seztique/' 

The reader is cautioned aflfainst supposing that the consequence alleged 
above does result from Gordan's researches, which are indubitably correct. 
This supposed consequence must have arisen from a misapprehension on 
the part of M. de Bruno of the nature of Professor Cayley^s rectification 
of tne error of reasoning contained in his second memour on Quantics, 
which had led to results discordant with Gordan's. Thus error breeds 
error, unless and until the pernicious brood is stamped out for good and all 
under the iron heel of rigid demonstration. In the early part of this year 
Mr. Halstedy a Fellow of Johns Hopkins University, called my attention 
to this passage in M. de Bruno*s book ; and all I could say in reply was 
that ** tne extrinsic evidence in support of the independence of the equa- 
tions which had been impugned rendered it in my mind as certain as any 
fact in nature could be, but that to reduce it to an exact demonstration 
transcended, I thought^ the powers of the human understanding.'' 

At the moment of completing a memoir, to appear in Borchardt*s 
Joumfld, demonstrating my quarter-of-a-century-old theorem for enabling 
Invariants to procreate their species, as well by an act of self-fertilization 
as by conjugation of arbitrarily paired forms, the unhoped and unsought- 
for prize fellinto my lap, and I accomplished with scarcely an eflfort a task 
which I had believed lay outside the range of human power. 



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Proof of the Fundamenial Theorem of Invariards. 179 

and thereby to adyance the standards of the Science of Alge- 
braical Forma to the most advanced point that has hitherto 
been reached. The stone that was rejected by the boilders 
has become the chief corner-stone of the building. 

I shall for greater clearness begin with the case of a single 
binary quantic (a, J, c, . . . , l^je, yy. Any rational integral 
function of the elements a,byCf...l which remains unchanged 
in value when for them are substituted the elements of the 
new quantic obtained by putting a + hy instead of a in the 
original one, I call a Dinerentiant in a to the given quantic. 

By a differentiant of a given weight w and order jy I mean 
one in every term of whicn the combination of the elements 
is of the jtii order and the sum of their weights w, the weights 
of the successive elements (a, 5, c, . . . Z) themselves being 
reckoned as 0, 1, 2, . . , t respectively. 

The proposition to be proved is, that the number of arbitrar}' 
constants in the most general expression for such differentiant 
is the difference between the number of ways in which w can 
be made up with the integers 0, 1, 2, 3, . . . i (repetitions 
allowable), less the number of ways in which w— 1 can be 
made up with the same integers. We may denote these two 
numbers by {w : i^j), (tr— 1 : t,^) respectively, and their dif- 
ference by *A(tr : i,j\ Then, if we call the number of arbi- 
trary constants in the differentiant of weight w and order ^" 
belonging to a binary quantic of the tth order T)(w : t, J), the 
proposition to be established is that 'D{w : t,y)s= A(to : %,j). 

Let us use H to denote the operator 

and to denote the operator 

Then it is well known that the necessary and sufficient condi- 
tion for D being a differentiant in .ris that the identity ADssO 
be satisfied. 

Let us study the relations of CI and in respect to D. 

Li the first place, let U be any rational inte^:ul function of 
the elements of order ^' and weight w ; then I say that 

fl.o.u-o.n.u=(tr-2tr)u. 

For if we use * to signify the act of pure differential opera- 
tion, it is obvious that 

n • . u= (n X 0)U + (ni>0)u, 

0.fl.U=(flxO)U+(0*)U; 

N2 



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180 Prof. J. J. Sylveeter's Proof of the undemotutrated 

.'. fl.o.u-Ofi.u=((a*o)-(o*n))u 

^ial+ii-2)l 1^ +(»-4>^-...-(t-2)*^^ -24 

If now paP . ft* . (f . . . P, where p is a number, be any term in 
. U, we have 

p + g + r+ . . . +< »y I j^ hypothesis ; 
q+2r + ...+it>sto) "^ ''^ 

.-. ii.o.u-o.n.u, 

t. e. 

.f d ^,d , d ^ id\ 
Vdk+^S-^'di-'-^^dl) 

=2^(1; -2tr) (a^.b^.tf... P) 
=(t}'— 2w)U, as was to be proved. 

If now for U we write D a differentiant in a, we have 
nD=0, and therefore 

fl.O.D=SD, 
where 5=t/'— 2u^. 

Again, 

n.0(0.D)-0.n(0,D)=(v-2(ti? + l))0.D; 
for . D is of the weight w + 1; 

/. Q\ 0\ D=n • SD + (S--2)n . . D 
= (2S-2)ft.O.D 
=5(2S-2)D. 
Similarly it will be seen that 

a\ 0».D=S(2S-2)(3S-"6)D, 
and in general » 

a\ 0'.D=8(2S-2)(3S~6) . . . (^S-(?' + 9))D 
= (1.2.3...j)(S.ir^ S^=^...8-j-l)D, 

the successive numbers S, 2S— 2, 3S— 6, Ac. being the succes- 
sive sums of the arithmetical series 8, 8— 2, 8— 4, S— 6, &c. 



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Fundamental Theorem of Invariants^ 181 

To find the most general difierentiant in question^ we mnst 
take eveiy combination of the elemenis whose weight is w and 
orderj, of which the number is obviously {to : iyj), and prefix 
an indeterminate constant to each such combination ; then 
operating upon this form with il, we shall reduce its weight 
by unity, and shall obtain as many combinations of una 
reduced wei ght (th e order ^* remaining unchanged) as iliere 
are units in (tr— 1 : ijy Each of these combinations will have 
for its coefficient a linear function of the assumed indeterminate 
coefficients ; and in order to satisfy the identity iiD=0, each 
such linear function must be made equal to ze ro. There are 
therefore (w : ij) quantities connected by (to— 1 : ij) homoge- 
neous equations. Supposing the equati07is to be independent^ the 
number of the indeterminate coefficients left arbitrary is ob- 
viously the difierence between these quantities, viz. A(to : t,^'), 
The difficulty consists in proving this independence — a <fiffi- 
culty so great that I think any one attempting to establish the 
theorem, as it were by direct assault, in this fa^ion, would find 
that he had another Jrlevna on his hands. But a position thai 
cannot be taken by storm or by sap may be turned or starved 
into surrender; and this is how we shall take our Plevna. 
Be the equations of condition linearly independent or not, it 
is obvious that we must have D(w : f, j) equal to or greater 
than ^(w : i, j). I shall show by aid of a construction drawn 
from the resources of the " Imaginative Beason," and founded 
on the reciprocal properties that have just been exhibited by 
the famous and O, that this latter supposition, of the first 
member of the equation being greater than the second, is inad- 
missible and must be rejected. Observe that (0 : t, j), the 
number of ways of making up with j combinations of 
0, 1, 2, ... t, is 1 ; also that D(0 : t, j), the number of arbitrary 
constants in the most general difierentiant in ^ to the quantic 
(a, 6, <?, . . . yje, y)' of order j and weight is also 1 ; for such 
differentiant is obviously Xa*. 

Thus we have for all values of tr. 



and also 



J)(w : v)= or >(u^ : ij)-(w-l : i,f), 
D(0:t,;)-(0:»,i); 



.-. D(tt7:t,y) + D(u;-l:t,y) + D(tt7-2:t,y) + ... 

+ D(0 : ij)= OT>(w'. iyj). 

If in the above condition, for any assumed value of u^, > is the 
sign to be employed, then the equation D(w : t,y)=A(tr: t,/) 
cannot be satisfied for all values of w. If, on the other hancl^ 

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182 Prof. J. J. Sylvester's PTW>f of the undemonstrated 

> is not the sign to be employed, then this equation^ for every 
value of Wf comniencing witn the assmned one down to 0, 
must be satisfied. The greatest valne of w for given values of 

i,y, it is well known, is ^ for ij even, and ^ ^ for ij odd. 

Let us give to w this maximum value in the above " greater 
or equal " relation ; for brevity, denote the differentiants whose 
types are[w,t,;], [tii^,t,j] ...by [«?], [w^-l], [tr-2], Ac. 
respectively, t and j being regarded as constants. It will bo 
convenient to substitute u>r the number of arbitrary constants 
in any of these difierentiants the same number of linearly in- 
dependent specific values of them; so that we sh all have 
D^w: i,j) of linearly independent [tr]'s, D(tp— 1 : t,^) of 
linearl y inde pendent [w— IJ's, and so on. Now, instead of 
the D(w— J : t,/) differentiants [w7— y], let us substitute the 
same number of the derived forms (0*[i£?— y])'s. I shall prove 
that the quantities (all of the same weight le) thus obtained 
are linearly independent of one another. 

For (l5 suppose that those belonging to any one set 
0*. [w— j] are not independent, but are connected by a 
linear equation. Then, operating upon this equation with II*. , 
we shall obtain a linear equation between the quantities [to — g] 
for each quantity (fl^. 0*. [«?— y] being a numerical multiple of 

tttj— y]), which is contrary to the hypothesis. Again, let there 
e a hnear equation between the quantities contained in any 
number of sets of the form 0^[tr— j] for which m is the 
greatest value of q. Then, operating upon this with XI"*, it is 
clear that all the quantities in the sets for which g<fn will 
introduce quantities of the form n"*"*'[w— 9] where m— 5r> O, 
and which consequently vanish. There will be left, therefore, 
only quantities of the form [«?—?], between which a linear 
equation would exist, contrary to nypothesis, as in the pre- 
ceding case. Therefore all the quantities in aU the sets 
are linearly independent. But these are all of the weight tr, 

u e. 1^ or ^^^ J j^nd are therefore linear functions of the num- 
ber of ways in which the integers 0, 1, 2, 3, . . . t can be com- 
bined i and j together so as to give the weight w. Therefore 
being linearljr independent, as just proved, their number can- 
not exceed this last-named number, i. e. cannot exceed (w : t,y). 
That is to say, 

D(tt7 : ij) + l>(w-l : hj)+... +D(0 : iJ) 
cannot exceed (w : t, j). Therefore every one of the equations 



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Fundamental Theorem of Invariants. 183 

'D(w : iyj)=s6^(to : iyi) must be satisfied from the maximum 
value of to down to the value 0, which proves the great hitherto 
undemonBtraied fundamental theorem for a single quantic. 

For any number of quantics the demonstration is precisely 
similar at all points : there will be as many systems of i^j as 
there are quantics. (w : i^j : V^f : &c.) will denote the num- 
ber of ways of making up w with j of the integers 0^ 1, 2^ . . . i, 
with/ of the integers 0, 1, 2, ... i', and so on. The theorem 
to be demonstrated will be 

D(u^ ii,ji V,f : . . . )=A(t(7 : i,j : i' :/ . . . ). 
XI will become 2 (a-^ "^^^ T "*" •••/^ 

It will still be true that fl'. 0'. D, where D is a difierentiant 
in X (t. e. a function of the elements in all the given quantics 
which withstand change when these are transformed bv writing 
a'\rhy for x), is a numerical multiple of D; and D will be sub- 
ject to the identity flD=0. We shall still have 

T>(w : i^j : i',/ : . . . )= or > A(ta : iyj : i',/ : . . • ), 
and 

D(0:i,i:i^/:...) = (0:i,i:t',/ :...), 

and shall be able in precisely the same way as before to der 
monstrate the impossibility of 2j*J^ D(ir— * : i^j : t^/) being 
greater than {w : t, j : t', /:...), and so shall be able to infer bv 
the same logical scheme £i(w i iyj : i',/ :...) = D(tr : ij : t', j^ 
my extension of Professor Cayley's theorem^ whidi leads 
direct to the Generating Fractions given in my recent papers 
in the Comptes Itendus, 

In a series of articles which I hope to publish in the Ame- 
rican Journal of Pure and Applied Mathematics, I propose to 
give a systematic development of the Calculus of Livariants, 
taking a difierentiant as the primordial germ or unit. I have 
spoken of a difiiBrentiant in a, and of course might have done 
so equally of a difierentiant in y. If we call the former D,, 
it is canable of being shown, from the very natures of the 
forms and fl, that if the quantity ij—2wy which may be 
called the degree of D,, be called S, tnen O^D, becomes a dif- 
ferentiant in y. These may be termed simple difierentiants ; 
but the principle of continuity forbids that we should omit to 
comprise in the same scheme the intermediate forms OvD« or 
CfD^y through which simple difierentiants in x and y pa^s 
into each other. These may be termed mixed difierentiants ; 



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184 Prof. J. J. Sylvester's Proof of the undemonstrated 

(yj)g may be termed a differentiant jp remoTed (as we speak 
of cowtina once^ twice, &c. removed) from j?, whicn will be the 
same thing as 0*Dy (a differentiant j removed fromy) if j[) + y 
is equal to the degree, viz. y— 2w7. Now all these differen- 
tiants, whether simple or mixed, possess a wonderful property, 
which may be deduced by means of Salmon's Theorem, given 
in the Philosophical Magazine for August 1877, They are 
all, in an enlarged sense of the term. Invariants — in this sense 
to wit, that if the elements are made to undergo a substitution 
consequent upon or, as we may say, induced bv a general 
linear substitution impressed on the variables, whicn for greater 
simplicity of enunciation may be supposed to have unity for 
the determinant of its matrix, then every differentiant, whether 
single or double (the latter being equivalent to an invariant), 
and whether simple or mixed, Mill remain a Constant Func- 
tion of the Coefficients of the impressed substitution. To wit, 
if the differentiant be p removes from a: and q removes from y 
(so that its degree is p + g), and if the impressed substitution 
be Ix + Xy for x^ and mx^rfiy for y, where Z/i— Xm=l, then 
will the differentiant be a constant bipartite quantic in the two 
sets of coefficients ?, m and \, /i, of tne degree q iu the former 
and p in the latter — a theorem which amounts almost to a 
revolution in the whole sphere of thought about Invariants. I 
have borrowed the term " Imaginative Heason " from a recent 
paper of Mr. Pater on Giorgione, in which, as in many of 
those of Mr.. Symonds (I will instance one on Milton in par- 
ticular), I find a continued echo of my own ideas, and in the 
latter many of the very formulae contained in my * Laws of 
Verse,' where versification in sport has been made aBsthetic 
in earnest. Surely the claim of Mathematics (its ^^Andera- 
strehen ") to take a place among the liberal arts must be now 
admitted as fully made good. Whether we look to the ad- 
vances made in modem geometry, in modern integral calculus, 
or in modem algebra, in each of these a free handling of the 
material employed is now possible, and an almost unlimited 
scope left to the regulated play of the fancy. It seems to me 
that the whole of aesthetic (so far as at present revealed) may 
be regarded as a scheme having four centres, which may be 
treated as the four apices of a tetrahedron, viz. Epic, Music, 
Plastic, and Mathematic. There will be found to be a common 
plane to every three of these, outside of which lies the fourth ; 
and through every two may be drawn a common axis opposite 
to the axis passing through the remaining two. 

So far is certain and demonstrable. I think it also possible 
that there is a centre of gravity to each set of three, and that 
the lines joining each such centre with the outside apex will 



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Fundamental Theorem of Invariants, 185 

intersect in a common point the centre of gravity of the whole 
body of aesthetic ; but what that centre is or must be I have 
not had time to think out. 

Johns Hopkins Universitj, Baltimore, 
November 13, 1877. 

Postscript. — In the first fervour of a new conception, I fear 
that in the manuscript which is now on its way to England I 
may have expressed myself with some want of clearness or 
precision on the subject of pure and mixed differentiants. I 
will therefore add a few more explanatory and vaticinatory 
words on this subject, through the medium of which I catch a 

glimpse of the possibility of obtaining a simple proof of Gordan's 
leorem, just as through the medium of pure differentiants 
taken per se I caught a glimpse (almost immediately afterwards 
to be converted into a cei-tainty) of the proof of Cayley 's theo- 
rem given in this memoir. I conceive that what the ensemble 
of pure differentiants have done for the one, the larger en- 
aemble of all sorts of differentiants, pure and mixed, taken 
together, will enable me or some one else to accomplish for 
the other. 

. Any function of the coefficients of a quantic which is nulli- 
fied by the operation upon it of XI, which we may call the 
revector symbol, or in other words, whose first revect is zero, 
is a pure differentiant in x. So, of course, if nullified by the 
operation upon it of 0, which may be called the provector 
symbol, it is a pure differential in y. We may call ij—2wy 
where i is the degree of the quantic, / the order of a pure dif- 
ferentiant, and w its weight in or, the grade of the differentiant, 
and denote this grade by S. 

The 8th provect of a pure differentiant in x is of course a 
pure differentiant in y, which is 8 removes from x^ as the pure 
differentiant in a; is S removes from y. If q be less than S, the 
q\ih provect of a pure differentiant in ^ is a mixed differentiant 
q removes from .r, or, if we like to say so, (8— y) removes 
from y. The grade of a mixed differentiant may be defined to 
be the same as that of the pure differentiant of which it is a 
provect or revect. 

Then, in the first place, we have this proposition : — If any 
linear substitution whatever be impressed in the variables of 
a quantic, the transformed value of any of its differentiants 
will separate into two factors, of which one will be the deter- 
minant of substitution raised to the power tr, where w is the 
weight corresponding to the order and grade of the differen- 
tiant and the degree of the quantic. The remaining factor 
will be a function of the coefficients of substitution, and may 



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186 Prof. J. J, Sylvester's Proof of the undemanstrated 

be called the oatstanding factor. Of this I shall proceed to 
speak. 

Let a be replaced by hx+ltfj 

y „ „ hx-^-my. 

Then the outstanding factor for the transformed D (a pure 
differentiant in x of uie grade £) may be proved by repeated 
applications of Salmon's theorem to be equal to 

where of course the series of terms in the development will, 
after the (S + l)th term, vanish spontaneously. In other words, 

KO. 

the outstanding factor of the transformed D is vrfe » .D, 
where it will be noticed that only the coefficients of substitu- 
tion due to the change in y make their appearance. 

If now we take any mixed differentiant, say the yth provect 
of D, i. e. Of. D, its outstanding factor, I find, will be the jth 
emanant of the outstanding factor for D, t. «. will be 

KO. 



{4.<J{-''^> 



And here for the present I end. The subject is, as it was, a 
vast one; and this conception of mixed differentiants opens out 
still vaster horizons. Every thing grown on American soil or 
bom under the influence of its skies, as its lakes, its rivers, its 
trees, and its political system, seems to have a tendency to rise 
to colossal proportions. 

I will merely add one remark which has occurred to me 
relating to Sturm's theorem and the process of Algebraical 
common measure in general. lSf{x, y) be a rational integral 
function of ar, v, Hiidf(x,y) its derivative in respect to x, and 
we perform the process of common measure between them 
regarded as functions of x, we know that the irreducible part 
of the successive remainders taken in ascending order, say 
Uo^UijUa,..., will have for their leading coefficients (say 
Dq,Di,D2...), the discriminants of / ana of its successive 
derivatives in respect to x respectively. 

Here D^ is an invariant of the given form ; 

Di (a differentiant in x) will be the leading coefficient 
of the covariant 



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Fundamental Tliearem of Invariants. 187 

D) 6^iiother differentiani in a) will be the leading co- 
efficient of the covariant 

D.**40D^y+ ^%D^/+ 3-^D,^+ ^^.D^, 

and 80 on until we come back to the first Stnrmian remainder of 
(j?,yy, the irreducible part of which (or we may call it the 
Sturmian Auxiliary Proper) is the Hessian diflFerentiated down 
from being of the degree 2t— 4 to the degree t — 2, i, e. to half 
of what it was at first ; and so in like manner every Sturmian 
Auxiliary Proper is, so to say, a Covariant difierentiated down 
to half its original dimensions. 

The above invariant and the following covariants may be 
called Yq, Vi, Vj, . . . respectively. The interesting point in 
question is that (to numerical factors pres) 

and so on. 

So more generally for any two functions /if.3?,y), ^(^,y), 
the irreducible part of the remainders obtainea by common- 
measuring them with respect to a will all be derivatives in 
regard to a of covariants of the two given quantics. If we 
take for our quantics 

• (a, 6, c, ... A, k, l\xy yy : (o^, 6', dy... //, *', V^x, y)', 

the covariants in question will all be edncts of (t. e. functions 
having for their leading coefficients) the successive resultants 
of the forms 

[(a,.../,, i, 0,(0'.... //,*', /')], 
of the forms 

[(a,...A,i), (a',.../.',*')], 

of the forms 

[(a,... A), (a',.../.')], 

and so on, the discriminants of which may be called partial 
resultants of the given forms ; in a word, the simplified residues 
arising in the process of commonmeasuring in respect to one 
of their variables two given binary quantics are differential 
derivatives, in respect to that variable, of the educts of their 
partial resultants (of course with the understanding that the 
last simplified residue is the complete resultant itself). 

This seems to point to the existence of some generalized 
statement of Sturm's theorem in which the same Educts as 



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188 On the Fundamental Theorem of Invariants, 

above referred to shall appear, but where, instead of their deri- 
vatives in respect to one of the variables being made use of, 
perfectly general Emanants of them shall be employed as the 
Criterion functions. For I need hardly add that all Educts 
(although not written so as to show it in what precedes) are in 
fact symmetrical in respect to the two sides of the quantic to 
which they belong. 

On various a priori grounds I suspect the generalized 
theorem to be as follows. If X,^ is the covariant (of degree 
2fJL) whose /ith derivative in respect to a; is a Sturmian Auxiliary 
Proper to F(j:, y), we may substitute throughout for all the 
values of /i, instead of each such derivative, the more general 

f-. y j~) Xa^j where /and j are any assumed positive 

constants, of course with the understanding that the second 

criterion also is to be (/ -7 g -r- j/in lieu of -1— • And the 

method of Sturm will still be applicable for finding the posi- 



. X 



tions of the real roots of - in /(^,y) — when we use these 

more general derivatives as the criteria instead of Sturm's 
own. When ^=0 the theorem is that of Sturm ; when/=0 
it is an immediate deduction from this theorem applied to 

finding the positions of the root values of ^, when it is borne 
in mind that the motions of - and of ^ as regards ascent and 

y ^ 

descent (excluding the moment for which either of these ratios 
is indefinitely near to zero) are inverse to each other. It is 
this that accounts for the negative sign which precedes g. 

It is difficult to conceive by what theorem other than the 
assumed one the chasm between those extreme cases can be 
bridged over; and all analogy and all belief in continuity vetoes 
the supposition that no such bridge exists. " Divide et impera " 
is as true in algebra as in statecraft ; but no less true and 
even more fertile is the maxim ^^ auge et impera,'^ The more 
to do or to prove, the easier the doing or the proof. 

November 19, 1877. 



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[ 189 ] 

XXVI. Elfictromaffnetic and Cahrimetric Absolute Measure- 
ments: the Absolute Value of Siemens' s Unit of Resistance in 
Electromagnetic Measure; the Relation between the Current- 
work and the Heat-evolution in stationary/ Galvanic Currents ; 
and the Absolute Values of some constant Hydroelectromotive 
Forces in Electromagnetic Measure. ( Condensed Comparison 
of the Results' of a Series of Investigations,) By H. F. 
Webbr, Professor of MatJiem/Uical and Technical Physics 
at the Federal Polytechnic Academy of Zurich. 

[Concluded from p. 139.] 

IV. Absolute Values of constant Hydroelectromotive Forces. 
{Third Procedure for the absolute Determination of the 
Siemens Unit of Resistance.) 

HAVING given in the foregoing the experimental proof 
that the mechanical work consumed in the flow of sta- 
tionary galvanic currents, when there is no other action of the 
current, indeed finds its exact equivalent in the heat produced 
by the current, a new path can be entered in order to deter- 
mine the absolute values of galvanic resistances and constant 
hydroelectromotive forces. 

I. Measure the quantity of heat Q, which is produced by 
the current t (measured absolutely, according to any system 
whatever) in a conductor whose resistance is Wj which forms 
part of a circuit, during the time z ; the absolute value of the 
resistance w (measured according to the same system) is then 
to be calculated from the equation 

II. If the ratio of the resistance w to the sum of the resist- 
ances v\ of the rest of the circuit be then ascertained by means 
of an appropriate procedure, the heat produced in the entire 
circuit by the constant current i during the time z will be ob- 
tained in the expression 



^(«)-=(i+^)- 



If E denotes the sum of all the electromotive forces of the cir- 
cuit, according to Ohm's and Joule's laws, combined, 

J2(Q)=t^2(w?)r=tE^ 

holds good. For the absolute determination of the sum of the 
electroxnotive forces in the circuity or, more briefly, for the 



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190 Prof. H. F. Weber on Electromagnetic and 

absolute determination of the electromotive force active in the 
circuity we obtain the equation 

JQ(l+5)=iEz. 

III. If we then determine, according to one of the galvanic 
methods usually employed, the value of the same electromo- 
tive force in relative measure (let e denote this value) — say, 
on the basis of the absolute electromagnetic unit of current 
and the Siemens unit of resistance, — ^men by combining the 
two measurements a new mean will be obtained to determine 
the absolute electromagnetic value of the relative unit of re- 
sistance made use of: the absolute value of the latter is 

1S.M.U. = ~. 

e 

provided that the current-intensity i in the equation 

JQ(l + ^)=t-Ec, 

which served for determining E, was likewise measured accord- 
ing to electromagnetic measure. 

1 have carried out a series of absolute and relative measure- 
ments of the electromotive forces of the elements of Daniell 
and Bunsen according to procedures II. and IIL, in order to 
be able to derive the absolute value of the S. M. U. by a third 
method totally diflferent from the two already described. When 
selecting this process I had a secondary object also in view — 
to submit to as rigorous a trial as possible the correctness of a 
singular result obtained by M. Favre, which directly contra- 
dicts a great number of galvanic experiences. In this opera- 
tion one of my pupils, M. Rudio, rendered me important as- 
sistance. 

In the circuit of the Daniell or Bunsen pile employed, con- 
sisting of 7-10 elements, the platinum wire wound upon a 
hard^um frame, previously used, was placed in the already- 
mentioned water calorimeter. The resistance w of the pla- 
tinum wire was known accurately for all <he temperatures 
employed. The resistance Wy^ of the rest of the circuit, in 
which, as an essential part of the resistance, the pile was com- 
prised, was determined simultaneously with the electromotive 
force of the latter, by a process resembling that described by 
Mr. Mance*. A path for the current was constructed after 
the fashion of Wheatstone's bridge-process ; the place of the 

• IVocoedingv of the Royal Society, voL six. 1671, p. 248. 



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Calorimetric Absolute Meamrements. 191 

pile in Wheatstone's scheme was taken by a sensitive galva- 
nometer; that of the resistance to be measured in Wheat- 
stone's plan was occupied by the pile whose resistance and 
electromotiye foi*ce were to be measured, the single tangent- 
compass (B=s 165*7 millim.), and the other wire resistances 
which were indaded in the resistance w^. The resistances of 
the measuring-wire and the galvanometer branch had been 
accurately ascertained. With the bridge open and the rest of 
the circuit closed the galvanometer and the tangent-compass 
indicated certain deflections. The point of connexion of the 
bridffe-wire with the measuring-wire was now so chosen that 
the deflection of the sensitive galvanometer remained invari- 
able whether the bridge was open or for an instant closed. As 
soon as this point was found, according to known rules, first, 
the resistance w^ (in S. M. U.), could be determined, which the 
pile employed, the tangeni-compass, and the wires belonging 
to them possessed at that determinate current-intensity t'l 
which had been indicated by the tangeni-compass with the 
bridge open; secondly, the electromotive force exhibited by 
the pile when traversed by the current t'l could be calculatea 
in relative measure (founded on the absolute electromagnetic 
current-unit and Siemens's unit of resistance). 

After this the absolute value of the same electromotive force 
was determined, by means of the amount of heat which it ge- 
nerated in its circuit by a current t, maintained constant (which 
was always approximately =ii), during the time z. For this 
purpose the pile, the tangent-compass, and the wires which 
were also comprised in the resistance wi were combined with 
the platinum resistance w in the calorimeter to form a circuit, 
through which the constant current i then passed during the 
time z. The quantity of heat Q, which this current would 
have called forth during this time in the calorimeter if the 
platinum resistance had possessed, not the alternating tempe- 
ratures of the calorimeter, but the constant temperature ta of 
the environment, is, according to equation (2) in section III., 

Q=Mc«[^-^o+B(^"-^.>]= -J— 

This heat was calculated from M, c., ^, T, t^^ tay and z by the 
previously indicated process. 

Immediately after the conclusion of the calorimetrical mea- 
surement, the resistance t^i and the electromotive force e were 
measured a second time in relative measure according to the 
above-described procedure, in order to control any variation 
in the two quantities that might have taken place during the 



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192 Prof. H. F. Weber on Electromagnetic and 

time z and bring it into the calculation. Such variations were 
regularly ascertained ; but they did not exceed very narrow 
limits. As these small variations of Wi and e have their phy- 
sical cause in processes which run proportionally with the time, 
it is permitted to put, instead of their mean values during the 
time z^ the mean values given by the initial and final observa- 
tions. If the initial values of the relative electromotive force 
and the resistance w^ be called respectively ^ and w/, and the 
final values ef' and w?/', understanding by E the mean value 
of the absolutely, and by e that of the relatively measured 
electromotive force, and let w^ represent the value of the pla- 
tinum resistance corresponding io the temperature f« of the 
environment of the calorimeter, we have for the determination 
of the quantities E and e the two equations : — 



and 



JQ[i.=^f"]=^. 



« = 



From this we can derive the absolute value of Siemens*s 
resistance-unit : 

1 S. M. U. = -• 

e 

I give in the following the results of the experiments wliich I 
have carried out with the cooperation of M. Rudio. In the 
calculation of the experiments J was supposed equal to 428*55 
m.-k., equal to the mean of the values resulting from our 
experiments on galvanic heat-evolution and from the experi- 
ments on the thermal behaviour of the pennanent gases. 

Experiment 1. Bunsen's element. — freshly amalgamated zinc, 
sulphuric acid of sp. gr. 1*035, commercial nitric acid of sp. 
gr. 1*365, gas-coal. 

1(7/ =7*683 S. M. U., V= 7*449 S. M. U., «'= 19*873, 

e^^= 19-734, E = 18*885 x ioio("^^"m.5mmigr.\ 

\ sec* / 

Mean values. 
1^1= 7*566 «= 19*804. 

Besult. 

1 S. M. U. = ? =0-9536 X lO^^/'?'^! 
e \ sec. / 



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Calorimetrie Absolute Measurements. 193 

Experiment 2. The same element with the same filling. 
tri'=7-411 8. M. U., V=7-279 S. M. U., «'=20'094, 

e"=20-007, E=19-150x 10^'>( """°'*i"g^-* ). 

\ S6C« / 

Mean Talues. 

^1=7-345 ^= 20-050. 

Result ■ 

1 S. M. U.=0-9552 X lO^of ^^^HH^: ). 

\ sec. / 

Experiment 3. Darnell's element — freshly amalgamated zinc, 
snlphuric acid of sp. gr. 1*035, concentrated solution of sul- 
phate of copper, copper. 

«7/=6-949S. M. U., V=7-081S.M. U., <j'=11-952, 

e''=ll-741, E=ll-286xlO^«(5i™lEglLL) 

\ sec* ' 

Mean yalues. 
1^=7-015 e=ll-847» 

Result. 

18.M.U. =0-9526 xlO^«(H^^-). 

\ sec. / 

Experiment 4. The same element with the same filling. 
ici'=6-831 S. M. U., trx"=7-125 S. M. U., c'=ll-887, 

«"=ll-739, E=ll-317xlO^' ("^"''°-*,°'g"-\ 
' • \ sec' / 

Mean yalues. 

tri=6-978 «=11'814. 
Result. 

1 S. M. U. =0-9579 X lo^of 2HilEi). 

\ sec. / 

Experiment 5. Daniell's element — freshly amalgamated 
zinc, concentrated solution of sulphate of zinc, concentrated 
solution of sulphate of copper, copper. 

<=16-598S.M.U., V=16-039S.M.U., €^=11-453, 

.''=ll-450, E = 10-954xl0^o( millim.«mgr.\ 

\ sec. / 
Mean yalues. 

tffi= 16-319 «= 11-451. 

Result, -. 

lS.M.U.=0-9565xlO^'>CHi^^-\ 

\ sec. / 

Pha. Mag. S. 5. Vol. 5. No. 30. March 1878. 

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N 



194 Prof. H. F. Weber on Electromagnetic and 

The determinations execnted according to this third method, 
of the absolute electromagnetic value of Siemens's mercury 
unit, have given the following results : — 

IS. M.U. =x 0-9536 xlO^« 
„ =0-9552 „ 
„ =0-9526 „ 
=0-9579 „ 



9} 



„ =0-9565 „ 
The mean value from these experiments amounts to 

lS.lLU.=01«»OxlO«'(5?il^). 

\ sec* / 

For fiicility of review, I place the final results for the abso- 
lute value of the S. M. TJ, together. We have found the ab- 
solute electromagnetiG value of: — 

1S.M.U. =0-9545 xlO^<?2H«E:) 

\ sec. / 

from 18 series of experiments^ in whicb the variable currents 
generated by magneto-induction were employed ; 

1 8. M. U. =0-9554 x 10" (^^^) 

\ sec. / 

from 24 series of experiments, in which the variable currents 
called forth by sudden voltaic induction were employed ; and 

1 S. M. U. =0-9550x 10^^ 0^^\ 

\ sec. / 

from 5 series of experiments, in which the heat-production of 
stationary galvanic currents was used. 
The general mean, 

1S.M.U. =0-9660x10^^(5*^), 

\ sec. / 

is only i per cent, greater than the result found by Messrs. 
Maxwell, Jenkin, and Stewart. After these results I hold 
that the questions of the true absolute value of the S. M. U., 
and whether the British resistance-unit does or does not repre- 
sent the value asserted, are settled. The true value of S. M. U. 

liesbetweenO-9536 x lO'^fH^^^^ andO-9550 x loiofHl!!!!!?:). 
V sec. J \ sec. /' 

and the British unit represents, neglecting very minute difier- 

ences possibly still present, the value asserted, 10^^ (— y 

When an observer finds the same result in three difierent 

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Calorinietric Absolute Measurements, 195 

ways, and employing three quite diiFerent natural laws — ^when, 
farther, this result but very slightly differs from that of another 
group of observers who worked according to a fourth, essen- 
tially different method, ceiiainly it can be pretty safely main- 
tained that the result so found is correct. 

In instituting this last series of experiments, besides ascer- 
taining the absolute value of the S. M. U., I pursued also, as I 
have already intimated, another aim, which, in conclusion, I 
will briefly explain. 

M. Favre has repeatedly determined with the aid of the 
mercury calorimeter the quantities of heat developed by the 
most various electromotive forces in their circuits during the 
time in which they consume equal quantities of zinc — ^namely, 
the quantity which is chemically equivalent to the unit of mass 
of hydrogen. As the result of his experiments, he found that 
the ratio of those quantities of heat gives quite another value than 
does the ratio of the corresponding electromotive forces when 
measured galvanometricallt/. Thus, according to M. Favre, 
the quantities of heat which the elements of Daniell and Grove 
produce in their circuits during the time within which they 
consume 1 equivalent of zinc are 23993 and 46447 units. 
The ratio of these numbers is 1 : 1*93, while the electromotive 
forces of the Daniell and Grove elements stand (according to 
all galvanometric measurements hitherto executed) in the ratio 
of from 1 : 1-68 to 1 : 1-70. This result of M. Favre's directly 
contradicts certain galvanic laws which are universally re- 
garded as resting on a secure foundation, as will be evident 
from the following consideration : — 

If E denotes ihe hydroelectromotive force of a circuit, w the 
sum of all the resistances Of the circuit, and Q the sum of all 
the quantities of heat which the constant current t calls forth 
in the circuit during the time z, then, according to Joule's 
law (which we have demonstrated under section III. to be 
correct), 

or, if, according to Ohm^s law, we put ttc^sE^ 

JQ=iE^. 

If a denotes the electrochemical equivalent of zinc, the quan« 
tity m of zinc which is consumed within the element during 
the time z becomes, according to Faraday's law of electrolysis, 

llierefore the total heat Q produced in the entire circuit by the 

02 



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196 Electrumoffnetic and Calorimetric Absolute Measurements, 

electromotive force B during the time that within the element 
the qnantity m of zinc is consuming is 

Hence, if the galvanic laws of Joule, Ohm, and Faraday are 
universally true, the quantities of heat Qi and Qs which two 
different electromotive forces Ej and Ej develop in their cir- 
cuits during the time they consume equal quantities of zinc 
muift be in exactly the same proportion as the electromotive 
forces El and E3. Consequently M, Favre^s measurements and 
the three laws mentioned are irreconcilable tvith each other. 

M. Favre's results are refuted by the above-stated determi- 
nations. The relative values of the electromotive forces, mea- 
sured by a galvanometric method, have been found to be;— 

For Bunsen's element, in the mean, 

^1=19-927. 
For Daniell's element with sulphuric acid, in the mean, 

€s= 11-830. 
For Daniell's element with sulphate of zinc, 

^3=11-451. 
And the absolute values of these electromotive forces, deter- 
mined simultaneously by the heat generated in the entire 
circuit, have given : — 

For Bunsen's element, in the mean, 

19-017 X loWmiUimtinmigrA ^ j,^ 
\ sec. / 

For Daniell's element with sulphuric acid, 

11-301 X Wo(E^E^^SEl)=e,. 
For Daniell's element with sulphate of zinc, 

10-954 xlO>o r"'°'^"/"^^-V E»- 
\ sec. / 

From these we get for the ratio of the galvanometrically 
measured electromotive forces and the electromotive forces 
measured by their heaircvolution the values 

^=1-684, ^«l-740, ^ = 1-033, 
1=1-683, 1=1-737, 1=1-031, 



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On Ram-Chrnds and Atmospheric Electricity. 197 

numbers which rigorously correspond to ihe deductions from 
the laws of Ohm, Joule, and Faraday. The cause of Favre's 
result being so seriously faulty lies probably, in great part, in 
the circumstance that, in all his calorimetric investigations, he 
made use of the mercury calorimeter ^ with the use of which a 
whole series of uncertainties are necessarily connected, and 
which it shoald be a maxim not to employ. For all galvano* 
calorimetric investigations in which the duration of tioe heat- 
evolution can be chosen entirely at discretion, and so the heat 
produced can be made as great as we please, the simple water 
calorimeter, managed with nicety, is by far the most reliable, 
and, for many reasons, even preferable to Bunsen's ice calori- 
meter. The numerous measurements instituted by M. Favre 
many years since, respecting heat-production bv galvanic cur- 
rents and electromotive forces, were very probably all vitiated 
by an error of the same order as were the values given by him 
for the heat developed by Daniell's and Grove's elements. 
Should a secure basis be obtained in this department, nothing 
remains but to repeat with more accurate methods all the more 
important of his measurements. 

The unit of length employed in these investigations is the 
millimetre of the cathetometer of the Physical Laboratory at 
Zurich; the time-nnit is the second of mean time; the Siemens 
resistance-unit is the No. 1914, which I obtained from M. W. 
Siemens at the commencement of the investigation, and which 
was most carefully compared with all the other resistances 
employed. 
. Zurich, AuguBt 1877. 



XXVIL Rainr-Clouds and Atmospheric Electricity, By W. B. 
Aybton and John Perry, Professors in tlie Imperial Col-' 
lege of Engineering^ Tokio, Japan, 

To the Editors of the Philosophical Magazine and Joumal, 

The Imperial College of Enjnneeringy 
Gentlemen, Tokio, Japan, December 8, 1877. 

/^ lyiNG all due weight to the theories of thermoelectric 
vT currents produced by rotation of the earth under the 
sun, and of currents which might be produced by moving 
electrified shells of air, we have always thought that these 
sources of electric disturbance on the earth were far too incon- 
siderable to give rise to the phenomena of earth-currents and 
of atmospheric electricity, and also totally inadequate to 
account for currents of suflScient intensity to produce ter- 
restrial magnetism. We think that there cannot be any 



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198 Professors J. Perry and W. E. Ajrrton on 

explanation of these phenomena which does not take into 
account the fact that the earth and other members of the solar 
system are the electrified coatings of condensers^ since, althongh 
the mutual coefficients of induction between the different 
members of the solar system may be very small compared 
with the capacities of long telegraph-cables, still the oiffer- 
ences of potential between the sun and the planets may 
be extremely great, so that the charges in the condensers in 
question may be so large that a slight change in the capacities, 
produced by rotations or changes in the positions of the pla- 
nets, may set up in the bodies themselves electric currents of 
considerable magnitude. 

We are at present engaged in the solution of the problem to 
determine mathematically what is the strength of the currents 
produced in the earth as it rotates under the inductive action 
of the sun ; and we may mention that the moderate conduc- 
tivity of the earth, combined with the probability of the exist- 
ence of an iron core, will enable us very shortly to present the 
results drawn from our theory in a numerical form. In the 
meantime, however, we desire to show how it follows from 
this theory that movements in the atmosphei-es of the earth 
and sun, and especially the motions of rain-clouds, or clouds 
of vapour, are connected with the phenomena of atmospheric 
electricity and earth-currents. The connexion of these latter 
phenomena with earthquakes, which we dwelt on in our recent 
paper on observations of atmospheric electricity, will more 
suitably be taken up again in our next paper. 

When a dielectric is composed of air at different pressures, 
or of a mixture of gases, our experiments (recently communi- 
cated to the Asiatic Society of Japan in a paper on the 
Specific Inductive Capacity of Gases) showed tnat K, the 
specific inductive capacity of the medium, is different at differ- 
ent parts, so that {see C. Maxwell's * Electricity ') flie fun- 
damental equation connecting the potential Y and p the charge 
of electricity per unit volume of the medium at different points, 

Consequently, if there is no real charge in the medium, we 
have 

Now, if we imagine the non-homogeneous dielectric to be all 
replaced by dry air at 7C0 millimetres pressure and at 0° C. 
temperature, and if at any point where the potential is V there 



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Bain^Clouds and Atmo^herio Electrieity. 199 

is an imaginary charge p' such as would prodnce the actual 
distribution of potential that we have in the real case^ then 

d?+^-^d?-+*^'^-^- ... (3) 
From equations (2) and (3) we find 

'^ dx da dy dy dz dz ^ 

or if f> is the density per unit volume of a real charge at any 
point of the non-homogeneous dielectric, then 

4irKo'-47r +^.^ + ^.^ + ^.^. 
^^ ^ '^ dx dx dy dy dz dz 

Also if at any place there is a dbtinct separation by a sur- 
face of one dielectric from another, ordinary air from very 
moist air for example^ then the resultant forcQ on one side of 
the surface must be greater than that on the other. Thus, if 
the resolved part of uie resultant force in a direction at right 
angles to this surface be F in the first medium and F' in the 
second, and if K and K' are the specific inductive capacities, 

KF=KT'. 
In fact it is the same as if both media were dry air as above, 
and an apparent charge, of density o^, were given to the sur- 
face, Bucti that 



iw-'->- 



If at the surface there is a real charge of density a-, then 

KF=K'F+47r^; 
and the action is as if both media were air as above, and an 
apparent charge of density </ were given to the surface, where 

These formulae may be used, when we know the state of the 
atmosphere at every point at every time (that is, when the 
specific inductive capacity K is known), in order to find from 
any given initial distribution of potential the changes which 
occur when the state of the atmosphere is changed. 

It is known that, from observations of atmospheric elec- 
tricity and from observations of earth-currents, atmospheric 



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200 On Eain-Clouds and Atmosplieric Electricity. 

changes may be predicted (see oar paper on Observatioo 
Atmospheric Electricity, read before the Asiatic Societ; 
Japan, April 25, 1877). And we see from the above i 
tions why this should be the c^se, since changes in the 
of the atmosphere, whether brought about by actual motijj 
or by alterations of density from cooling, or from other < 
must produce changes in the specific inductive capacity 
dielectric, ^nd consequently alterations of the potential 
earth in the neighbourhood. Assuming dry air at 760 
lims. pressure and at QP C. temperature to have a spe 
inductive capacity unity, then as we mix some aqueous 
with it the specific inductive capacity increases and 
larger than 1 ; and in addition, as some of the vapour 
denses, we know that the globules of water, excessively sif 
at the beginning, soon increase in size, so that, as the sp 
inductive capacity of water is some millions of times tl 
air, the mean specific inductive capacity of the space is 
mensely increased ; and hence we see that the cooling of I 
atmosphere and the formation of clouds, or the approachl 
clouds, may occasion great changes in the distribution^] 
atmospheric potential at any place, and consequently give n 
to strong earth-currents. And if the cloud has no cnargel 
its own, the direction of these currents will be such that po 
tive electriciiy will flow from the place from which the clo 
is passing to that from which it came ; for since the earth^ 
known to be negatively electrified with regard to space, ' 
introduction of a cloud or other dielectric of greater spec 
inductive capacity than air must make the potential of 
part of the earth s surface underneath it less negative 
before — that is, must raise the potential. 

Although mere changes in the density of the air will, 
the reasons given above, be sufficient to produce earth- 
rents, still we should imagine that the changes in the k\ 
spheric potential commonly observed are due, not so much i 
the direct change of the specific inductive capacity wit 
change of densit}"-, as to the much greater changes that mud 
be produced in me capacity by the tormation of cloudy result 
ing from the change of temperature and density ; so that wi 
should expect that observations of atmospheric electricity will 
be of greater use in the predicting of rain and snow than < 
wind-storms. 

As the atmosphere does not altogether consist of non-con- 
ducting matter, portions of it, especially cloudy portions, are^ 
capable of acquiring electric charges, through cnanges of tern- " 
perature or motions of the atmospnere ; and these portions sub- ' 
sequently become more or less conducting through changes of J 



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Digitized by VjOOQIC 



Phil Mag. S. 5. Vol. 5. PI. VIII. 



Fi 



y>< 


JU.3. 

^^ nothMrmud,. 


Fig. 4. 


1 

1 


x^ 


V v^ 


/ 


Jf^ 


V 


J^ r 


^f-^ 


V 


V 


T 


p^ 


==" "h 


\ 



Fig. 7. 



2f 



Fig. 8. 



A^# 



Fig. 11. 
PF S W D 

ami. 
Steaan. \ SUam, 




led 



r 



ice 

artd. 

StMom 



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li^uitem Bros Hth. 



On a new Modification of the Bichromate Battery, 201 

temperature : we here see an explanation of how thunder-clouds 
may be formed. It is probable, however, that in the ordinary 
phenomena of atmospheric electricity and earth-currents the 
real charges possessed by portions of the atmosphere may have 
but little effect ; but on this point we cannot at present express 
a decided opinion. 

We beg to remain, Gentlemen, 

Very truly yours, 

John Perry, 
W. E. Ayrton. 



XXVIII. On a new Modification of the Bichromate Battery, 
By H. C. Russell*. 

[Plate Vra. fig. 14.] 

Sydney Obsevvatory, 

My dear Sir, May si, 1877. 

TOU were kind enough to advise me, when I was in 
England, about the purchase of a large Buhmkorff coil. 
In using it, I have had the ordinary bichromate-of-potash cells 
to develop the electricity, and of course have had to suffer the 
inconveniences which attend the use of a cell which falls off so 
quickly. This has induced me to look for a more constant form 
of electric generator ; and I have found one that is perfectly 
constant in its action, and will remain so as long as the solution 
and zinc are supplied. I enclose a section-drawing ^Pl. VIII. 
fig. 14); tad you Will see I have adopted a modification of one 
of Daniell's earliest ideas for obtaining a constant current. The 
solution used is the ordinary bichromate of potash, in the 
arrangement shown, which perhaps needs little explanation ; 
but I may say that a drop of solution per second keeps the cell 
in full and steady work. The drawing is at fault in one 
respect ; the only space in the cell for solution is between the 
plates, not, as shown, all round the plates : the object of this is 
to make all the solution pass the face of the zinc You will 
observe that, supposing the waste-tap shut and the drop- 
tap above openeaj the solution accumulates in the cell till 
it comes to the level of the overflow-pipe; and then, for every 
drop which goes in, one goes out ; but as the overflow-pipe 
begins at the bottom of the solution, it is the used or waste 
solution which must go out. When the battery is not required, 
the waste-tap is opened and the other shut, and the batters'- 
cell is left perfectly inactive and ready for the next time it 
is wanted. There is of course some additional first cost ; but 

* Communicated by Dr. Hoggins, F.It.S. 

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E 



202 M. A. Rittor*8 Contributums to the Study 

I fiud the convenience and certainty of action far oyerbalance 
this. 

I send it in the hope that you may find it nsef al ; bnt should 
on know of any more convenient electric generator^ I shall 
e moch obliged if you will let me know. On the other hand, 
if the foregoing is something new and you think it worth pub- 
lication, I leave it entirely in your hands to do as you like. I 
had hoped to be able to send you a copy of some work I have 
been doing with the spectroscope ; but tiie mail closes before I 
am ready^ and I await another opportunity. 
Believe me, my aear Sir, 

Yours faithfully, 
Dr. Hugginsj H. C. KUSSSLL, 

Sfc. 4'c. 

XXIX. ContribtUions to the Sttidy of States of AffffreffcUion. 
By A. Bitter*. 

[Plate Vm. figs. 1-13.] 
§ 1. Temperature^urface of Air, 

IF a kilogram of air at rest is confined in a cylinder by a 
movable piston, its pressure p, volume v, and absolute 
temperature T are, by the gaseous laws, connected by the 
the equation 

i"'=IlT, (1) 

the constant B being equal to 29*27 when t; is expressed ia 
cubic metres andj? in kilograms weight per square metre. 

This equation shows that the quotient y^ has always a con- 
stant value, however the state of the air may be altered by 
shifting the piston or applying heat. 

For the absolute temperature of the air we have from the 
above equation the expression 

i=f « 

The magnitude T appears in this equation as a function of 
the two variables p, v ; and the law of the alteration of T with 

?and V can be exhibited geometrically by a curved surface. 
f the point in the horizontal plane X if whose coordinates 
are p, v is found, and a perpendicular to the plane of length 
T drawn through it, the extremity J of this perpendicular 

• From PoMpendorfTs Armaleny No. 10, 1877 ; translated and commu- 
nicated by Robert £. Bajnes, M.A., Senior Student of Christ Church, 
Oxford, and Lee's Reader in Physics. 



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of States of Aggregation. 203 

may be taken to represent the state of the air at the given 
moment (fig. 1^ PI. VlII.). Sappose this constmction repeated 
for all values ofp^v; then the geometrical locus of all the 
points on which the extremity J can lie is a carved surface, 
which for shortness may be called the ^^ temperature-^turfaeeJ*^ 
To every point of this surface corresponds a particular state of 
the air, since a particular value of each of the variables />, r, T 
18 given when the position of the point is given. 

Through the point J draw a plane parallel to the vertical 
plane i Z ; the temperature-surface is cut by this plane in 
a straight line whose inclination c to the plane of ^ v is given 
by the equation 

*^*=^ = R' ^3) 

in which v is to be considered constant.. 

Again, draw a plane through J parallel to the vertical plane 
OXZ ; its line of intersection with the surface is also ^^rai^rA^, 
its inclination being given by 

^^=d^ = R> (*) 

wherein p must be taken constant. 

Thus tiie lines of constant volume and the linos of constant 

Pressure on this curved surface form two systems of straight 
nes. The temperature-«urface can therefore be conceived as 
the geometrical locus of all the intersections of these two sys- 
tems of lines. 

If, finally, we draw a horizontal plane through the point J, 
the temperature-surface will be cut by it along a curved line 
which represents a line of constant temperature (as it corre- 
sponds to the equation T= const.), and may therefore be 
termed an ^' isotliermal " (fi^. 2). The equation of these iso« 
thermals may also be given m the form 

pvss const., (5) 

whence it appears that an isothermal lies in a horizontal plane 
and is a rectangular hjrperbola. 

If we consider the temperature-surface as the face of a 
mountain, the isothermals will be represented by curved hori- 
zontal paths along its slope, while the lines of constant volume 
and the lines of constant pressure are straight paths leading 
directly up the slope. Each given alteration in the state of 
the air may then be looked upon as a movement over the moun- 
tain by a given path whose successive points represent the 
successive states tnrough which the air passes. 



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204 M. A. Hitter's Contributions to the Study 

§ 2. Isothermah of Water-vapour. 

The temperatare-surfaoe of the so-called perfect gases is, as 
was shown in the preceding paragraph with reference to atmo- 
spheric air, a surface continuously carved in all its parts. The 
temperatore-snrface of steam is, on the contrary, a curved sur- 
face with edges. 

As its temperature falls, steam passes into the liquid and 
solid states of aggregation. To these changes correspond 
changes in the law of curvature of the temperature-surface, 
which will accordingly appear as a curved surface made up of 
several surfaces of continuous curvature. 

We get a clear conception of the difference between vapours 
and perfect gases by likening their temperature-surfaces to 
mountain-faces as before. In the higher regions the forms of 
both mountains would most probably be approximately the 
same, since we may assume diat at very hign temperatures 
steam behaves like a perfect gas. Considerable differences 
between the two forms, however, will make an appearance 
lower down, since, in the mountain which represents the beha- 
viour of water in its three states of aggregation, the uniformity 
of the continuously curved slope is broken by sharp-edged 
cliffs and steep walls of rock that stand out and project cor- 
nice-like, wholly changing the character of the landscape in 
the lower regions. Consequently also the horizontal paths, 
that run along the mountain-slope and represent the isother- 
mals, will in Sie lower regions differ very considerably in form 
from the isothermals of perfect gases. 

If superJieaied steam undergoes isothermal compression, and 
the law of alteration of its pressure p with the volume v during 
the motion of the piston is represented geometrically by a line, 
then this line runs on at first just as in the case of atmospheric 
air. At the point M, however, that corresponds to the pas- 
sage of the vapour into the saturated state, the line will form 
an angle (fig. 3). Condensation begins at this position of 
the piston, and the pressure p remains constant when the 
piston is pushed further in. The following part of the iso- 
thermal will therefore be a straight line parallel to the volume- 
axis V. This straight line M N extends to the point N cor- 
responding to the condensation of the last particle of steam. 
Here the isothermal forms another angle ; for the pressure of 
water increases with extraordinary rapidity when its volume 
is diminished. This last piece of the isothermal will there- 
fore be a curve that rises up very steeply from the axis of 
abscissae. 

In passing from the isothermal T to the isothermal T+dT 



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of States of Aggregation. 205 

each of the two angalar points M and N will describe a line- 
element that belongs to an edge of the temperature-surface 
(fig. 4). Analogous edge-formations will appear on the sur- 
face at those points that correspond to the passage from the 
liquid into the solid state of aggregation. Hence it follows 
that the temperature-surface for water in its three states of 
aggregation cannot be represented, as that of perfect gases, by 
a single equation of simple form. Such an equation will rather 
represent in all cases only a portion, more or less limited, of 
the whole temperature-surface. 

§ 3. Isobars and Isothemials of the Ice^egion. 

K a vertical plane is drawn parallel to the vertical tempe- 
rature-axis OT and to the horizontal volume-axis OV, and 
therefore perpendicular to the horizontal pressure-axis O P, its 
intersection with the temperature-surface is an " isobar " or 
line of constant pressure. Such an isobar will in general 
contain two straight horizontal lengths or segments, of which 
ihe upper corresponds to the vaporizatuyn and the lower to the 
freezing of water. As horizontal lines on the temperature- 
surface represent isothermals, each of these horizontal seg- 
ments is also an isothermal segment. 

Thus, for instance, for the isobar corresponding to the con- 
stant pressure of one atmosphere the upper horizontal segment 
coincides with the isothermal for 100^ C, and the lower with 
tlie isothermal for 0^ C. (fig. 5). The length of the upper 
horizontal segment represents the expansion (about 1650-fold) 
that attends vaporization ; the length of the lower represents 
the expansion (about 9 per cent.) that occurs when water 
freezes. If a vertical line is drawn through a point of the 
lower horizontal segment, we see that under certain circum- 
stances three different temperatures can correspond to the 
same volume under given pressure, since the line of constant 
pressure is cut three times by the vertical line. 

When the pressure increases, saturated steam experiences a 
rise in temperature, but melting ice a/att in temperature. 
Hence in tne isobar for a pressure greater than one atmo- 
sphere the upper horizontal segment will take a higher position, 
but the under one a lower position. If, then, the temperature- 
surface is again represented by a mountain-face, that part of 
the mountain which represents the passage from the liquid to 
the solid state of aggregation will appear as a wall of rock that 
juts out and projects like a cornice (fig. 6). 

Consider a horizontal plane drawn through the lower part of 
this temperature-mountain ; its line of intersection with the sur-^ 
face will be an isotliermal of some such form as that in fig. 7; 



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206 M. A. Ritter'8 Contributions to the Study 

just like the isobar, it has/otir angdar points and two straight 
segments, the meaning of which is obvious when we consider the 
gradual transformation under an isothermal compression of a 
mass of water out of the state of superheated vapour, first into 
the solid and then into the liquid state of aggregation. The an- 
gular point M corresponds to the passage of the vapour from 
the superheated to the saturated state ; the straight segment 
M N exhibits the gradual passage from the vapour to the solid 
state of aggregation (snow-formation). The point L marks 
the beginning of melting that only starts under higher^pres- 
sure ; and the straight segment L iL represents the gradual pas- 
sage from the solid into me liquid state of aggregation. 

The isothermals of the ice-region are therelore distinguished 
from the isothermals for higher temperatures (that are repre- 
sented in fig. 7 by the dotted line) by having three angular 
points N, L, K, instead of one, J, as in the latter. We pass 
from the one group to the other at the isothermal which cor- 
responds to a temperature higher than 0° C. by 0-00744°; and 
this isothermal must therefore be couqted among those of the 
ice-region. This limiting isothermal corresponds to the tem- 
perature (0^*00744 C.) at which water freezes or ice melts 
under a pressure equal to its vapour-tension (comp. § 5)*. 

Thougn isothermals may in general be likened to hori- 
zontal pailis on a mountain-face, this comparison is unsuitable 
in the case of the isothermals of the ice-region as they stretch 
along the under surface of an overhanging diff. 

To the temperature 0^*00744 C. corresponds a vapour-ten- 
sion of 0*006 atmosphere. If we draw the successive isobars 
(as in fig. 6) for continually smaller pressures, we shall find^ as 
shown later, that for the pressure of O'OOG atmosphere the two 
straight segments coincide, since each will coincide with the 
straight segment of the isothermal for 0^*00744 C. For still 
smalfer pressures the isobar takes the form in fig. 8. There 
is but one straight horizontal segment in this line ; and it cor- 
responds to the direct passage from the vapour into the solid 
state of aggregation. 

§ 4. Edges of the Temperature-s^irface, 

Consider the successive isobars drawn as in fig. 6, or the 
successive isothermals as in fig. 7; the angular points of these 
lines make up edges of the temperature-surface. These edges 
bound the three regions on the surface which correspond to 
the three different states of aggregation. These three regions, 
however, do not directly border on each other, but are sepa- 

* [This peculiarity was first pointed out by Professor Pliicker in the 
Proceedings of the Royal Society for 1874, p. 457.— Tb.] 



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of States of Aggregation, 207 

rated by three regions of transition (figs. 9, 10, 11). Each of 
these three regions of transition has the form of a cylindrical 
surface whoso generating lines are parallel to the volume-axis ; 
Tiewed, therefore, in this direction, it appears a line Tfig. 10). 

As regards the water-edge JW and the steam-eage LD, 
we may assume that they meet at a certain height (near the 
isothermal for 410° C, according to Cagniard de la Tour), or 
subside into the surface ; for it is exceedingly likely that at 
very high temperatures there is no difference between the 
liquid and gaseous states of aggregation*. 

To each point of the temperature-suriace correspond defi- 
nite yalues of the coordinates p^ v, T ; and by these three 
values the state of the whole mass is in general unambigu- 
ously defined. An important exception, however, occurs in 
the case of those points that lie on the straight segment J K L 
of the isothennal for 0°-00744 C. or of the isobar for 0-006 
alanosphere. This segment (which is represented in fig. 10 by 
the point J) corresponds to those values of the pressui-e and 
temperature at which water can simultaneously exist in all 
three states of aggregation f- If^ then, the pressure, tempe- 
rature, and volume of the whole mass be given by any point 
on this segment, the internal condition of the mass is not suffi- 
ciency denned, since a knowledge of the total volume is not 
sufficient to determine ike proportions in which steam, water, 
and ice are mixed together. As, further, the intrinsic energy 
(die innere Wdrme) of steam is considerably greater than 
that of water, and this latter than that of ice, the intrinsic 
energy of the mixture is by no means defined by the position 
of the point, an infinite number of values of the intrinsic 
energy corresponding indeed to each single point of this 
segment. 

Thus, for example, the point K of this segment may repre- 
sent the state of 1 kilogram of water which &s increased 9 per 
cent, in volume by freezing throughout ; or it may represent 
the state of this mass after a 9-per-cent. increase in volume by 
partial vaporization. In the latter state, however, the mass 
would possess about 80 calories more of intrinsic energy tlum 
in the former state. 

This straight isothermal and isobaric segment J K L (figs. 9 
and 11) forms an edge of the temperature-surface along its 
whole length ; and as this edge is distinguished from all the 
other lines and edges of the temperature-surface by the above- 
mentioned remaruible properties, we shall call it in future the 
*^ principal edge of tJve te^nperature^surface.^^ (Following J. 

* Andrews, Pogg. Ann, Erganzbd. v. p. 64. 

t The pomt J was on this account named the trifle paint by J. Thomson. 



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208 M. A. Bitter's Contributions to the Study 

Thomson's nomenclatnFe for the point J of fig. 10, we might 
also caU it the triple edge). 

We mav further call the steam-edge L D the cloud-^-ge^ 
since the beginning of condensation is marked by the format 
tion of a cloud; and the water-edge JW may be called the 
rain-edge or the dew-edge, since the product of complete con- 
densation exhibits itself as rain or dew. The edge F J may 
be conceived as the line on which water begins to freeze, and 
may therefore appropriately be called the Jrost-edge. The 
edge S K can be conceived as the line in which ice begins to 
melt, and may therefore be called the melting-edge. The edge 
R K may be called the rime- or snouo-edge, as the product of 
the direct transformation of aqueous vapour into the solid state 
appears as rime or snow. 

To conclude, exact proportions could not be given in the 
above figures, from the nature of the case ; for if, for ex- 
ample, the segment J K, so as to be perfectly discernible, wer^ 
drawn even only one millimetre long, the segment K L would 
have a length of more than two kilometres on a diagram drawn 
exactly to scale. 

§ 5. Angles formed at the Principal Edge. 

By Clapeyron and Clausius's law the relation between the 
pressure and temperature of saturated steam can be expressed 
by the difierential equation 

dT AmT' ^^^ 

where r denotes the latent heat of steam, u the increment of 
volume that occurs on vaporization, K^-^-^ the heat-equiva- 
lent of a kilogrammetre. To the value T=273 (or <=0) cor- 
respond the values r= 606*5 and ws= 210*66 *. In the iso- 
thermal for 0° 0., therefore, the above difierential coefiicient 
takes file value 

dp _ 424x606-5 ,... >y.. ,g. 

(fT "■ 210-66 X273""**'^'' ^^> 

If the principal edge (represented in fig. 10 by the point J) 
lay exactly in the isothermal for 0° C, then would the above 
value be the tangent of the angle marked <^ in that figure. 
As the point J really lies on the isothermal for 0°"00744 C. 
(as will appear later), the above coefiicient, in order to repre- 
sent tan ^ exactly J requires a slight correction, which we can 
easily make by determining from tables by interpolation the 
values of r and u that correspond to T= 273*00744 (or 

* Zeuner'B Qrtmdaige der mechanischen Warmetheorie. 

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of States of Aggregation. 209 

<= 0-00744) and repeating the above calculation with these 
values ; we then find for 3ie angle ^ the more exact equation 

tan<^=4-483, or <^=77°25' (3) 

Equation (1) can also be used for the passage from the solid 
into the liquid state of aggregation^ if for u the increment 
(negative) of volume that occurs on melting and for r the 
latent heat of water are substituted. The latent heat of water 
has the value * 

Z=80 (4) 

for the pressure of one atmosphere and the melting-point 
f 0° C.) corresponding to this pressure. In melting, the mass 
aiminishes in volume by 

U=s0-00109 -O-OOl = 0-00009 cubic metre. . (5) 

Hence, on substituting ^u for +u and I for r in equation (1); 
we obtain the differential equation 

%=^-m ^^^ 

as the relation between the pressure and melting-point, I and 
II beinc functions of T. To the temperature T=273 corre- 
spond uie values given in (4) and (5); and on substituting these 
we obtain for the value of the differential coefficient 

jf-=-aSSf3=-1380545. . . (7) 

To a pressure-increment therefore of 1380545 kilograms 
weight per square metre (or 183'6 atmospheres) corresponds 
a lowering of the melting-point by one degree C, if the dif- 
ferential coefficient does not alter in value for this change of 
temperature f. It follows that near the principal edge the 
band of the surface which lies between the frost- and melting- 
edges^ and represents the mixture of ice and water (fig. 9^, 
makes a very small angle with the horizontal plane, since an 
extremely small lowering of the isothermal for the melting- 
point corresponds to a very considerable increment of pressure* 
The angle marked -^ in fig. 10 differs therefore only very little 
from a right angle. 

To a diminution of the pressure by the weight of 1 kilogram 
per square metre would, by equation (7), correspond a rise 
of the melting-point by iggJiftjiK degree. When, therefore, the 
pressure diminishes from 103o3 to 62*58 kilograms weight 

* Wiillner, Experimentiilphifsik, 2nd ed. iii. p. 548. 
f Clausius, Meckamsche Wiirmeiheoriej 2nd ed. i. p. 173. [This result 
was first shown by Professor J. Thomson. — Ta.], 

Fhil Mag. S. 5. Vol. 5. No. 30. March 1878. P 

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?. 



210 M. A. Bitter's Contributions to the Study 

er square metre, the melting-point rises from the isothermal 
or ^sO to that for 

'=^^SiF=0-00744 (8) 

Since at this temperature the pressure of saturated vapour is 
also 62*58 kilograms weight per square metre (or 0*006 atmo- 
sphere), it follows that the principal edge coincides with the 
straight segment of the isothermal for '00744 C. and of the 
isobar for 0*006 atmosphere pressure. 

The rime^ge RK (fig. 9) can be conceived as the line 
along which the direct passage of ice into the gaseous state 
begins. In applying equation (1) to the sublimation of ice, 
we have to put r + Z in place of r, and t/ — u in place pi u ; then 
for the relation between the pressure and the sublimation-point 
of ice we have the differential equation 

^r^ACtt-lOT w 

In the isothermal forO^ C. this differential coefficient takes die 
value 

dp_ 424x(606-5+80) _..nfi /im 

(/T"" (2io-66-u-oouuy)x273'~*'^"' • • v^^; 

from which the corresponding value for the isothermal for 
t = 0*00744 differs by an insignificant quantity. For the angle 
marked di in fig. 10 we therefore have 

tan «= 5*06, or (0=78° SO' (-11) 

The angle © is thus greater than the angle <^ by 1° 25'*. 

Hence it follows that ifce principal edge is a prominent edge 
in the part K L, but a receding edge in the part J K. 

We shall naturally find values for the angles <^, '^y to essen- 
tially diflFerent from the above when we employ a difiTerent 
unit in measuring either jp or T in the construction of the 
temperature-surface. If, for instance, we choose one atmo- 
sphere as the unit of pressure, denoting by n the pressure in 
atmospheres, then we nave 

dp = 10333(/n, (12) 

and we obtain with this system of units the following equa- 
tions for the angles: — 

tan<^= 0*000434, or ^= 0^ r 30"; . • (13) 
tan'^^=133*6, or^=89°34'; . . . (14) 

tano>== 0*00049, or©= 0° 1' 41'^ . . (15) 

* Compare Eirchhofi^ I'^gPT* -^^^^ ^ii- P* 206* 



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of States of Aggregation. 211 

§ 6. Diacontinuily on crossing the principal edge. 

In general we may represent a given change of state by the 
motion of a point along a definite line on the temperature- 
surface^ and the law followed by the mass in changing state 
defines the form of the path-curve. 

If at everjj point of the temperature-surface the state of the 
mass as well as the position of the point were defined without 
ambiguity when the values of the three coordinates were given, 
then might every line on the temperature-surface be consi- 
dered as representing a continuous change of state, since to 
the passage along an infinitely small element of the path cor- 
responds only infinitelj' small variations in the magnitudes 
that characterize the state of the mass. If the line were to cut 
an edge of the temperature-surface, it might still serve to 
represent a continuous change of state even at the points of 
intersection, although the law of change would in general un- 
dergo a sudden alteration as the edge was crossed. 

By § A^ihQ principal €d^« represents along its whole length 
the singular cases of exception wherein the above condition is 
fwt satisfied. To every given point of this edge indeed corre- 
spond definite values of the coordinates j3, t?, T ; but to each 
of these systems of values correspond an infinite number of 
different values of the intrinsic energy U. Here, therefore, a 
change of state can occur without any accompanying change 
of coordinates. 

Considering the infinitely small line M N, cutting the prin- 
cipal edge, to represent an element of the path that represents 
the change of state, we see that in the passage from M to N 
the magnitude U jumps discontinuously from a greater to a 
smaller value, while- the pressure, volume, and temperature 
change only infinitesimally (fig. 12). The initial point M just 
above the principal edge represents a mixture of water and 
steam^ and the point N just below the edge a mixture of ice and 
steam. . To each of tkese points corresponds a definite value of 
U; and the difference between these values is finite^ reaching 
a maximum of more than 80 calories when the edge is crossed 
at the point K. To a continuous variation of U would corre- 
spond a discontinuous motion of the point representing the 
state of the mass. On arriving at the principal edge it would 
suddenly stop, remain there until the due variation of U was 
accomplished, and then continue its motion along a line lying 
at the other side of the edge. 

To represent this discontinuity we may consider the tempo- 
ratui'e-stirfece' cut along the whole length of the principal 
edge, and conceive this edge as a double edge made up of two 

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212 M. A. Hitter's Contributions to the Study 

parallel edges lying infinitely near each other*. The two 
parallel edges may be considered as separated by a crevasse 
that reaches a maximnm depth at K, gradually snallowing to 
zero towards J and L — the term depth not being taken in its 
actual sense, but figuratively [since there is no real variation 
ofT]. 

§ 7. Adiabatic passage over the principal edge. 

When a mixture of water and steam expands adiabatically, 
the temperature and pressure continuously diminish till the 
temperature falls to <= 0^*00744. At this instant the water 
begins to freeze, and the heat that is thus set free prevents 
any further fall of temperature while any part of tne mass 
remains liquid. The adiabatic will thus form an angular point 
at M where it reaches the principal edge, and its next piece 
will be a straight horizontal length comciding with the prin- 
cipal edge (fig. 13). After the mixture of water and steam 
has been changed into 4i mixture of ice and steam, the tenipe- 
rature and pressure begin anew to fall. The extremity N of 
the horizontal length M N is therefore a second angular point 
on the adiabatic. 

The motion of the point along the horizontal length M N 
represents a change of state during which part of uie water 
freezes while anomer part vaporizes. The heat set free daring 
the freezing of the first part goes to vaporize the second. If 
^1 denotes the mass of steam in the condition M, and x^ de- 
notes the mass of steam at the end of the change M N, then 
1— a?j is the mass of water frozen and ^j—^i the mass of water 
vaporized. The vaporization of the latter requires the^heat 

Q=K^«-«i); (1) 

and the heat set free during the freezing of the first part has 
the same value, 

Q=:7(l-^,) (2) 

On equating these two values and solving the resulting 
equation for ^s, we obtain 

_ Z + rxi 
^«- i^r • • W 

The change of ^3 ^ Xy kilograms of water into steam increases 
the volume by 

rj-.vi=u(^ji— ^1); (4) 

and the work thus done by the steam-pressure is 

5l=/>tt(^a— ^1) (5) 

• C. Neumann, Vortemngen uler die mcchanische WSrmetheorie, p. 150. 

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of States oj Aggregation, 213 

This work, which is represented in fig. 13 by the shaded rect- 
angle^ is eqaivalent to the heat 

y=Ajtni(4r,-^i) (6) 

Here p= 62-58, 1^=210, /=80, r= 606-5; and on substi- 
tuting these values in the above equations we get them in the 
forms 

a?,= 0-1165+ 0-8835 ori, .... (7) 

f,-i;i=24-5(l-;ri), (8) 

y= 3-61(l-a'0 (9) 

If, for instance, the whole mass were at first liquid, so that 
jissQ, we have in this case 

a?,=0-1165, r,-ri=24-5, ^^=3-61. 

In the adiabatic change of a kilogram of water into a mixture 
of ice and steam, therefore, 0*1165 kilogram will vaporize and 
0*8835 kilogram freeze ; 3*61 calories of the intrinsic energy 
will be turned into external work; and the increment of volume 
represented in fig. 13 by the length M N will be 24*5 cubic 
metres. 

§ 8. Coficlrmon, 

As a result of the above discussion, there follows the theo^ 
retical possibility of representing the behaviour of water in its 
three oifferent states of aggregation by a solid geometrical 
figure, even though considerable difficulties would be encoun- 
tered in the exact practical execution of such a model by reason 
of the insufficiency of the experimental results already in 
hand*. 

The same procedure as this we have followed for water may 
also be adopted for representing the behaviour of any other 
body by a model of its temperature-surface. As the ground 
of such a model we may take a hyperbolic paraboloid, which 
represents the behaviour of the so-called perfect gases, and 
pieces may be stuck on it to represent the difiering behaviour 
of other bodies. 

On the model for such bodies as expand in melting {e, g. 
sulphur, phosphorus, &c.) \he frost- edge will appear as a rece- 
ding edge, and the inelting-edge as a prominent one. Instead 
of the prominent cornice that represents the freezing-region 
on the water model, we shall find on the models for these 
bodies a terrace-shaped prominence to represent the same 
region. 

* A plaster model of the temperature-Burface of water, made by the 
sculptor Blum, of Aachen, is in the museum of the Aachen PolTtechnicum. 

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214 Mr. W. H. Walenn on Unitation, 

If the necessary data were known from experiment for all 
bodies, we might then exhibit their behaviour in changing 
state by a series of models — just as certain of their properties 
ai'e naturally shown by their crystalline forms. 

Aachen, June 28, 1877. 



XXX. 'On Unitation. — ^VIII. Practical Remarks thereon^ 
together unth Examples. By W. H. Walenn, Mem. Phys. 
Soc. 

[Continued from vol. iv. p. 370.] 

29. TN the general formula for any integer number, given in 
JL art. 28, namely 

a»r»-* + a„_i»^-* + ... + a^f^ + a^r + aif 

the suffixes to the coefficients which correspond to the digits 
are so disposed as to show the number of digits at a glance. 
They also show, by inspection, the place of any one digit in 
the number, counting the unit's digit as the 1st digit, symbo- 
lized by aj, the tens' digit as the 2nd digit, symbolized by aj, 
the hundreds' digit as the 3rd digit, symbolized by a^j and so 
on. This use of the snffix implies a law; and the law is an 
extension upon that which has hitherto appeared in relation to 
suffixes ; this extension involves a special interpretation of the 
sjonbol aQ. 

In this place it must be noted that suffixes have not been 
used with that attention to perfect congruity which should 
accompany every mathematical work. In ordinary algebra, 
these adjuncts to notation have most frequently been used for 
the seines of coefficients in the general formula for an equation, 
or in an expression in which each term is presumed to have a 
coefficient, either known or unknown. In these cases, for the 
most part, the suffixes simply indicate the order in which the 
coefficients follow one another : sometimes this order is from 
the right hand to the left, and in opposition to the order of the 
indices of the powers of the unknown quantity or variable ; and 
sometimes it is in the same direction. A common use of the 
suffix is to mark the index of the power of the variable to which 
the coefficient belongs in any particular term. It is used in 
this way in Hind's ' Algebra ' (second edition), chap. xi. p. 374, 
for instance in the formula 

Another use of the suffix is to mark the terms that disappear 
when a particular operation is performed upon a general ex- 



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Mr.W. H. Walenn on Unitation^ 215 

pression ; this is the case in the formula 

sm(^a?D |X=: Ax^r— Aso:* + AjA**— A7a?^ + &c., 

derived from 

sin ^aDjX^sin C^ . jA^ + sin/^^ • 1 jAi^ + sin f^ . 2 jAjor' + AcJ 

Bat no fall recognition of the fanction of a suffix appears in 
any of these uses. When this method of indicating tne order 
of a series of quantities is completely developed, it should be 
capable of showing, not only the sequence and direction, but 
also the relative position of each member of the series to a 
given point, as in the case of the ordinal numbers, 1st, 2nd^ 
3rd, <&c. 

The use made of the suffix in unitation, as proposed in 
art 28, is in accordance with these views ; and, in the general 
formula for integer numbers above cited, the suffix expresses 
the order of the digits commencing with the unites digit, count- 
ing the unit's digit as the Ist integer digit from the decimal 
point, the tens' digit as the 2nd digit, &c. A question then 
arises which is as important, in relation to ordinal numbers, as 
the meaning of a® is in the theory of expouents. This question 
can be answered on a basis as logical as that of the exponen- 
tial question : it is, " If the series be continued towanis the 
right hand, as 

a^, rt«-i, On^iy a»i-3; &c. . . . Oj, ai, ttfl, a-i, a.j, Ac, 

what does a^ mean ? " It is impossible to think of the next 
number to ihe right of the unit's digit (which is in the Ist 
decimal place) as having any relation to Qq ; for as the unit's 
digit in the number is the 1st digit to the left of the decimal 
point, so the next figure to the unit's digit, on the right hand, 
IS the 1st digit to the right of the decimal point. If these 
suffixes are to be read as ordinal numbers, a^ must be left out ; 
for the 0th place to the right or left of the decimal point is the 
decimal point itself. That is, if the above general formula be 
extended to decimals (or towards the right hand), it must be 
written 

^li^"' + ««-i»^"* + • • • + a^r^ + ag^^ + «i^** + a_ir-* + a^^"^ + ... 

and aQ has no other meaning than the decimal point itself. 

Writing in the top row, which follows, an ordinary number 
with a finite number of decimal places, the corresponding co- 

* See Dr. Graves (Bishop of Limerick), ' Law's Matkematical Prise/ 
1853, quoted in Carmichaers * Calculas of Operations/ p. ICO. 



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216 Mr.W. H. WaJenn on Vnitation. 

efficients of the formula are represented in the underneath row 

as follows : — 



I 



7 4 5 
a, aj ai 



6 2 5 



Thus written, each ordinal suffix has due relation to the posi- 
tion of its corresponding digit, and the whole number, in 
respect to the suffixes, is read: — 5 is the 1st digit (from the 
decimal point understood), 4 is the 2nd digit, 7 is the 3rd 
digit. Then (in the opposite direction) 6 is in the first de- 
cimal place, 2 is in the 2nd, 5 is in the 3rd. 

Normally considered, the operation of unitation always pro- 
coeds from right to left ; but the negative suffix indicates the 
possibility of a change from right to left to left to right, under 
certain circumstances. This view will receive further consi- 
deration in the proper place. The use of Qq as determining 
the place from which tne direction of the operation is to be 
reversed, is believed to be new, and may be of use in other 
departments of mathematical science. Thus the meaning of 
Oq, in the series a^, a^, cj, a^, a_i, a»j, &c., is satisfactorily 
made out, according to the principles of the interpretation of 
symbols, to mean the place from which the order of the suf- 
fixes is reckoned, in reference to direction of counting. 

30. This interpretation of Qq may be well illustrated by a 
geometrical diagram : — If a vertical line cross a horizontal line, 
as in the marginal dia^ 
gram, in the style of Des- | 

cartes's rectangular coor- 



dinates, and if the origin «» • • • «8 «« «i «o ^-i ^-« • • • ^-» 
be taken as the point from i 

which the counting is to 

commence in both horizontal directions, namely backwards 
and forwards, it is evident that the a which is at the origin is 
a^j and that the a's with the positive suffixes are distant from 
the origin in the numerical oider of their suffixes ; also the a's 
with the negative suffixes are distant from the origin in the 
numerical order of their suffixes, the negative signs simply 
indicating that the counting of the suffixes is to proceed in the 
opposite direction to the counting of the positive suffixes. 
31. The substitution of (r— S) for r, in the formula 

a^?**"* + a»-,r""* + . . . + a^r^ + a^r + aj 
for a given number N, yields 
«n(^-8)""* + an^i(rS)'"^ + . . . + aj^(r^By + a2(rS) + aj. 
This is a number which has the same remainder to S as N has ; 



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Mr. W. H. Walenn on Unitation, 217 

for on expanding the (r— S)"* portion of each term by the bi- 
nomial theorem, it has S as a factor in every term of the ex- 
pansion (of any one term in the latter formula) except the 
first, which is tne same power of r as occurs in the correspond- 
ing term of the original value of N. 

32. In obtaining the remainder to S of N, the formula in 
art. 31 may be extended, by means of negative suffixes, into 

thus making it available for other numbers than whole num- 
bers. In the operation for obtaining the remainder, the number 
resulting from the first substitution of the digits in the formula 
is again subjected to the operation ; then this last number is 
again treated in the same way, and so on, each treatment ^ving 
a number less than the previous one, and divisible by o with 
the same remainder that N has. If this treatment be continued 
until a number less tban 8 is obtained, that number is the uni- 
tate of N to the base S. This is acconling to the definition of 
a unitate given in the Philosophical Magazine for November 
1868, p. 346. 

33. This method of obtaining the unitate of N is general, 
and is therefore valuable. It also afibrds a means of compa- 
ring the properties of U«N with those of N in a direct and 
satisfactory manner. 

The repetition of the process of reduction by the fonnula is 
peculiar to unitation ; and it may be symbolized by Ui'^-N, 
(n) being the number of times the formula is applied to a 
given determination of U^ N in order that the ultimate value 
of n«N may be less than S. This repetition has no analogy 
in the expression of a number by means of the formula N. 

The following examples illustrate the repetition of the pro- 
cess of reduction : — 

I. If N=: 1234567, 

W N=l + 2 + 3 + 4 + 5 + 6 + 7=28. 

WN=2 + 8=:10. 

WN=1 + 0=1. Here(n)=3. 

II. In obtaining UyN, if the fonnula containing the unre- 
duced powers of 3 be used, 

V^' N=3M + 3^2 + 3^3 + 3'.4 + 3^5 + 3. 6 + 7=1636. 

U/'N=3M + 3^ 6 + 3.3 + 6=96, 

U/''N=3. 9 + 6=33. , 

U7 N=3. 3 + 3=12. 

U; N=3. 1 + 2=5. Here(n) = 5. 

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218 ]Jfr. W. H- Walenn on Unitatioru 

III. If the formula with the reduced coefficients be em- 
ployed*, namely 

U7N = a? + 5a6 + 4a5 + 6a4 + 2a3 + Sex, + ai, 
then 

U7' N=l + 10 + 12 + 24 + 10 + 18 + 7=82. 

U/'N=3- 8 + 2=26. 

U/<'N=3. 2 + 6 = 12. 

F;* N=3. 1 + 2 = 5. Here(n)=4. 

34. In N, as soon as any value of a^^ is increased, by the 
successive addition of units, up to or beyond r, it is trans- 
ferred to the next higher term, or that containing the factor 
a»^i, by adding a unit to the higher term and placing the 

remainder to r, or of the division — , in the term in which the 

lower factor a» occurs ; that is, r determines the maximum 
value of On in each term. 

In U5N, on the other hand, B may be taken of any integer 
value in respect to r, and the formula will still be true, but r 
will have no power to determine the highest value of a^ in any 
term ; B is the only determinator of the maximum value of a« 
in any term. For illustrations of this see Philosophical 
Magazine, May 1875, p. 347, and the above instances of UjN 
and U7N. 

35. The value of S, whether integral or fractional, for instance, 
determines the degree and kind of discontinuity that exists in 
U5N. For example, in 17^67 = ^, ^ is taken, by inference, as 
the unit; the same occurs in 119^67 = ^. In U2^.25 = J=1^, 
^ is the unit. 

36. In regard to the arrangement of the terms, N gives 
simply the arrangement of a number in powers of r ; whereas 
U^N gives the arrangement of the same number in powers of 
(r— 8). In the most useful form of U^N, each power of 
(r— 8) is reduced by substituting for it its remainder to S. 

74 Brecknock Road, N., 
December 1877. 

• See Phil, Mag. May 1875, p. 347. 



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[ 219 ] 

XXXI. The Contact Theory of Voltaic Action, By W. E. 
Ayrton and John Pebry, Professors of the Imperial College 
of Enff^ineering, ToJdOy Japan. 

To the Editors of tike Philosophical Magazine and JoumaL 

The Imperial College of Eugineering, 
Gentlemen, . Tokio, Japan, December 14, 1877. 

'\\I HEN contributing his paper, " On the Difference of 
▼ ▼ Potential produced by the Contact of Different Sub- 
stances." to the Royal Society on May 22, 1877, Professor 
Clifton, of Oxford, seemed to be quite unaware of the elaborate 
series of experiments on exactly the same subject made by us 
in the winter of 1875, a full account of which was communi- 
cated in a paper on " The Contact Theory of Voltaic Action, 
Paper No. 1.," to Professor Sir William Thomson, May 6, 
1876, who at the British- Association Meeting at Glasgow of 
that year gave a public account of the method employed by 
us and the results we obtained, reserving our complete paper 
for the pages of the Proceedings of the Eoyal Society, 

If the investigation in question had been of merely ordinary 
importance, we should not have deemed it necessary to point 
out the priority of our experiments to those of Professor 
Clifton ; but wh^n the fact is remembered (a fact not very 
evident from Professor Clifton's papery that a series of expe- 
riments such as we performed clears up the long-standing 
discrepancies between the chemical and contact explanations 
of voltaic phenomena, and so is of extremely great importance 
in the science of energy, we trust we may be pardoned for 
claiming the priority due to us. Much of the ordinary original 
work performed in physical laboratories must, of course, be 
undertaken nearly simultaneously in different countries ; and 
our great distance from Europe necessarily places us in tl e 
unfortunate position of being some months in time behind 
other men who publish papers in the same societies as our- 
selves ; but in this particular case the work was not of an 
ordinary kind, and we have not to ask for the indulgence of 
scientific men in making allowance for our residence in Japan, 
seeing that, first, our paper reached England exactly one year 
before Professor Clifton^s communication was made to the 
Royal Society, and, secondly. Sir W. Thomson was so kmd 
as to give an account of our method and results to the 
British Association several months before Professor Clifton 
appears to have commenced his earliest experiments on the 
subject. 

ITie method of experimenting employed by this gentleman 
is essentially the same as that used by ourselves, with this im- 



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220 Professors W. E. Ayrtou and J. Perry on the 

portant differenoe, that whereas Professor Clifton only removes 
the plates of a condenser from a distance a apart to a distance 
b apart, we removed them to an infinite distance apart, and 
then put them in such a position that the original charge to be 
measured was doubled ; so that in fact our method was by far 
the most delicate, and was only limited in sensibility by the 
natural imperfections of mechanism. All this was clearly 
shown in the carefully executed drawing that accompanied our 
paper. The advantages we derived from the superior delicacy 
of our apparatus are seen if we examine, as may easily be 
done, the two papers paragraph by paragraph ; for the metals 
and liquids employed by Professor Clifton being the same as 
those used by ourselves, in every case that he in 1877 was 
only able to detect the difference of potentials, we in 1876 
published not only the sign but also the numerical value of 
the difference in question (compare pages 301 to 305 of his 
paper in the 'Proceedings of the Royal Society,' No. 182, with 
our paper). Considering, too, that the quantities of electricity 
to be measured are so small, and consequently the slightest 
loss of electricity is so serious, we fail to see what benefit was 
derived from using six insulating stems instead of only the 
two carefully protected rods of our apparatus. 

We observe that Professor Clifton assumes throughout his 
paper the " summation law of electromotive force," and that he 
was compelled to make such assumptions in consequence of 
his inability to measure directly with his apparatus the differ- 
ence of potentials between two liquids in contact. But if this 
be assumed, then we might have employed in our research the 
method of measuring the difference of potential of two liquids 
in contact that we have often, as early as 1874, employed as 
a lecture-illustration to indicate this difference. This method 
consisted in attaching to the terminals of a quadrant-electro- 
meter two platinum wires, of which the ends were respectively 
dipping into two liquids separated by a porous diaphragm ; 
but to make any use of the observations obtained from such an 
experiment, it must be assumed that the observed deflection 
of the electrometer represents the algebraic sum of the three 
contact differences of potentials such as might be measured 
separately. At first sight, not to assume this might appear to 
be a refinement of caution on our part; but in reality it was 
imperative to prove experimentally that this assumption was 
true when it was taken in connexion with the statements ge- 
nerally made by the supporters of Thomson's theory of con- 
tact. For example. Professor Fleeming Jenkin says, on p. 44 
of his ^Electricity and Magnetism': — ^** When a single metal is 
•placed in contact with an electrolyte, a definite difference of 



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Contact Theo^i/ of Voltaic Action. 221 

potentials is produced between the liquid and the metal. If 
zinc is plunged in water the zinc becomes negative, the water 
positive. Copper plunged in water also becomes negative, but 
much less so than zinc. If two metals be plunged in water 
(as copper and zinc), the copper, the zinc, and the water form- 
ing a galvanic cell, all remain at one potential, and no charge 
is observed in any paii of the system.' Consequently in 1875 
we discarded our original proposed method of experimenting, 
which was to use an apparatus somewhat similar to that em- 
ployed by Professor Clifton, as far as we can understand it 
without a drawing ; and we constructed the apparatus described 
in our paper, which enabled us to measure any single contact 
difference of potential, whether of a metal with a metal, or a 
metal with a liquid, or a liquid with a liquid, or a combination 
of any two or more contact. 

The very important fact that the rise of the difference of po- 
tentials between the plates of a voltaic cell on first immersion, 
when the circuit remains open, is due to the same cause as po- 
larization of the plates when the circuit is closed but operating 
in the opposite direction, as explained by Professor Clifton, 
was clearly stated by us in our paper in question under " the 
three states of a cell ;" and our subsequent papers showed that 
we considered this effect to be analogous with the so-called 
soaking in and soaking out in any dielectric, or what is called 
the residual charge in a Leyden jar — ^a subject to which we 
have been since devoting much attention. But we even went 
further ; for we found that even when the circuit was closed 
directly after immersion, there was first a rise of difference of 
potentials, followed afterwards by a fall ; and this is an expla- 
nation of a want of constancy observed in many cells, and 
notably in the two-fluid cell described by Professor Clifton, 
page 309. 

We take the liberty of observing that although a table of 
the difference of potentials of the terminals of different cells is 
of great value to practical men, still we should hardly have 
expected to find such a table at the end of Professor Clifton's 
paper with one number only (almost without exception) given 
for each cell, since he was quite aware that the difference of 
potentials between the electrodes alters from the first instant 
of immersion of the plates. Again, we do not understand 
how he can say that no current has passed ; for it is evident 
that a current may pass without the electrodes being externally 
connected. A table such as is given by Professor Clifton 
would be very valuable if it gave the difference of potentials 
between the electrodes when the plates had been, kept im- 
mersed for a sufficient length of time for the difference of po- 



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222 Mr. T. Bayley on Hie Colour Relations 

tentials to reach its maximum value ; but it would be more 
valuable if it gave in addition the time-rise of the difference. 
We confess, however, that it is only with exceptional cells 
that we have succeeded in getting on different occasions ex- 
actly the same results with the same combination. Such a 
table as we suggest, which would be a great improvement on 
that given by Professor Clifton, could of course be constructed 
by any one possessing an electrometer without employing any- 
special apparatus. 

In conclusion we notice, page 299, that Professor Clifton 
sees the necessity of changing his apparatus, which could not 
measure directly the difference of potential between two liquids 
in contact, before he can obtain satisfactory measures of the 
difference of potential in certain important cases. We may 
mention that although the apparatus employed by us in our 
investigation described in our paper of 1876 enabled us to do 
this with considerable accuracy, still we thought it advisable, 
in the summer of that year, to construct a new apparatus, the 
accurate results obtainable with which will form the subject 
of our next paper on this subject. 

We beg to remain. Gentlemen, 

Verj'^ truly yours, 

W. E. Aykton. 
John Pkrry. 



XXXII. On the Colour Relations of Copper and its Salts. 
By Thomas Bayley, Assoc. R.C.Sc.I* 

COPPER in solution, as is well known, imparts to tlie 
liquid a blue colour. In the case of the chloride the 
colour inclines to green, but becomes blue on dilution. Wish- 
ing to see what relation the light transmitted by such solutions 
bears to that reflected from the surface of the metal, I made 
the following experiments. 

An extremely dilute solution ofcupric sulphate having been 
prepared, it was placed in a glass tube closed at the end by a 
thin plate of glass similar to those used for covering objects 
under the microscope. The tube had a narrow side-tube near 
the bottom ; this was fitted with a piece of caoutchouc tubing 
and pinchtap, so that any liquid contained in the tube could 
be drawn off. A flat plate of copper carefully polished, first 
with trent sand and oil and then with rotten-stone, was 
. placed beneath the tube in such a manner that the diffused 

* Communicated by the Author. 



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of Copper and its Salts, 223 

daylight from a window was reflected from its surface verti- 
cally upwards through the tube. The length of the column 
of solution of cupric sulphate was then varied by letting out 
small portions at a time through the side tube. It was found 
that the plate of copper, viewed through a certain thickness 
of the blue solution, appeared like a plate of polished silver. 
This certainly tends to show that the colour transmitted by 
solutions of copper is complementary to that reflected by the 
metal. 

I now placed a hollow glass prism before the slit of a spec- 
troscope, in such a manner that the light passed through a 
strong solution of cupric sulphate contained in it before reach- 
ing the prism of the spectroscope. The accompanying sketch 
(flg. 1) shows the effect of this upon the spectrum. 



VioleC 




Sdw 



Solar speotmm 
afl«r pMsing 
throQgh copper 
solution. 



Absorbed 
portKon. 

All light less refrangible than the sodium-line is very much 
diminished by passing through the copj.er solution, wnile the 
rest seems unanected. 

. I next endeavoured to determine in what particulars the 
light reflected from copper differs from ordinary light; and for 
this purpose I comparea the reflection from a ponsLed sheet 
of copper with that from a piece of white note-paper. The 
result appears in fig. 2. 



Fig. 2. 



Bed. Tallow. 



Oreen. 



Blue. 



Violet. 





2ha 












] 


[> 



Spectnim of 

n flection 
fromoorper. 

Spectmm of 
reflection 
from paper. 



Limit o fiwUr 

The part of the spectrum to the red side of the D line is more 



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224 On the Colour Relations of Copper and its Salts. 

intense in the light reflected from copper than in the light re- 
flected from paper. The oth^r parts of the spectra were of 
equal intensity in each. The red in the spectrum from copper 
is lengthened out beyond the point at which the red disappears 
in the spectrum obtained from white paper or direct from a 
window. As far as could be determinea with the instrument 
at my disposal^ the sodium-line exactly forms the boundary of 
the absorption-band of copper in solution, and of the bright- 
red region in the spectrum of light reflected from the metal. 

The latter spectrum possesses all the characteristics of an 
ordinary one, with this exception, that its red region is inten- 
sified and somewhat lengthened out. 

These results confirm the conclusions drawn from the expe- 
riments described as made with the tube. In those experi- 
ments the excess of red light was absorbed by the metal in 
solution and white light passed through. Seyetid preliminary 
attempts to found a method of estimating copper upon these 
properties were made as follows : — ^Three tubeis, similar to the 
first described; were placed parallel and vertical above a po- 
lished sheet of copper ; they were protected from extraneous 
light by a cylinder of blackened card, closed at the bottom by 
a piece of card also blackened, and pierced by three holes for 
the passage of the tubes. The tubes were graduated from the 
bottom upwards. In one tube a column of the dilute copper 
solution was placed of sufficient length to just allow the colour 
of copper to pass through, while the column in another tube 
was sufficiently long to cause a faint predominance of blue. 
A poiiion of the solution of unknown strength being placed 
in the third tube, it was easy to adjust its length until the 
light passing through it was intermediate between the red 
shade of the first tube and the blue of the second. 

Other matters having intervened, I have been unable to 
proceed far in this direction ; but the results already obtained 
justify the expectation that the method would be of much 
value in approximately determining the strength of very dilute 
solutions of copper, such as those running from mines, from 
which the copper is precipitated by metallic iron. 

These experiments were conducted in the chemical labora- 
toiy of the Koyal College of Science, Dublin, by the kind per- 
mission of Professor Galloway. 



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[ 225 ] 

XXXIII. Notices respecting New Books. 

Photographed Spectra, One Hundred and Hiirty-six Photographs of 
Metallic^ Gaseous, and other Spectra, printed hy the Permanent 
Autotype Process. J?y J. Eand Capeok, A-S.-4.iS>. London: E.and 
F. Spon. 

^PHE work before us is a handsome octavo volume, consisting of 
-^ 37 plates of permanent photographs and 80 pages descriptive 
of the plates. There are about 85 photographs of metallic spectra, 
and 50 of spectra of gases. 

The metallic spectra extend mostly from H to a little beyond F, 
the red end of the spectra of course not being recorded by the pho- 
tographic process. They were obtained with a direct- vision spec- 
troscope with one compound prism of 5 prisms, and are thus spectra 
of small dispersion, th6 interval F to G occupying about 1^ inch in 
the photographs. The author remarks that his results " are not 
intended to be placed by the side of photographs of spectra of 
larger dispersion taken for comparison of the metals, study of the 
solar spectrum, &c. ; but they may perhaps prove useful to amateurs 
and others working with spectroscopes of small dispersion, for 
comparison of spectra in their general aspect, and for study of the 
points and peculiarities attaching to most spectra which are gene- 
rally brought out in our prints." 

The spectra of the metals were partly obtained from the spark 
between points of the metal, and partly from ignition of pieces of 
the metal in the electric arc given by 40 pint Qrove's cells. 

The former series includes Arsenic, Aluminium, Antimony, Bis- 
muth, Barium, Calcium, Cadmium, Copper, Indium, Iron, Lead, 
Magnesium, Mercury, Nickel, Palladium, Selenium, Silver, Stron- 
tium, Tellurium, Thallium, Titanium, Tin, Zinc, Zirconium. The 
spectra obtained from the voltaic arc (the more interesting series) 
are those of Aluminium, Antimony, Bismuth, Beryllium, Boron, 
Cadmium, Chromium, Cobalt, Copper, Didymium, Erbium, Gold, 
Indium, Iridium, Iron, Lead, Magnesium, Manganese, Molybde- 
num, Nickel, Niobium, Palladium, Platinum, Ehooium, Euthenium, 
Silver, Thallium, Titanium, Tin, Tungsten, Uranium, Vanadium, 
Yttrium, Zinc, Zirconium. 

Mr. Capron has earned the thanks of spectroscopists for the 
large amount of useful work which he has performed for them, in 
the way of preliminary investigation. No exact scale or measure- 
ments accompany the photographs ; and they will be chiefly useful 
in indicating by comparison with each other the lines which belong 
to particular metals, and the conditions under which particular lines 
are produced. In the investi^tion of the spectrum of any sub- 
stance, it is a great saving of tmie to begin with small dispersion, 
and afterwards to apply higher powers when it becomes an object 
to determine exactly the wave-length of particular lines. 

But although no exact measurements are given, and although the 
photographs vary very perceptibly in length, nearly all show lines 

^IiU. Mag. S. 5. Vol. 5. No. 30. March 1878. Q 

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22C Notices respecting Nexc Books. 

which can be used as Feference-lines, by measuremeut from which 
the wave-lengths of the metal-lines can be determined. 

Thus in all the spark-spectra the lines of air are present in large 
number throughout the spectrum. 

The possessor of /this book will find it an advantage to mark the 
wave-lengths of the lines in the air-spectrum, which can best be 
done on the enlarged photograph of the air-spectrum given in the 
extra plato at the end of the volume. 

The line at the red end (marked *' spark " in the scale on Plate I.) 

is the nitrogen double Hue kqqo [ • The next group in the large 

photograph is a group of nine lines, the third of which (the brightest) 
has the wave-length 4630, and the finer ones 4642, 4640, 4621, 
4013, 4607, 4601, 4596, 4591. In the second photograph on 
Plate I. there are between these a group of three lines, 4803, 4788, 
4779. The next conspicuous line in the large photograph is 4447, 
and then (with a faint band between) 4416. Then comes a broad 
mass of lines occupying some inch or so in length. The least-re- 
frangible bright line of this group (not the fine one) is 4348. The 
centre of the broad band is 4230, then a very close pair of lines, 
4190, 4184. Commencing now at the blue end of the spectrum, 
there is a solitary bright line 3995, then a hazy band the brightest 
part of which measures 4038, and then, easily recognizable in all 
the photographs, a double line (really triple) follow^ by a some- 
what wider double, and then three equidistant lines with a still 
wider interval. These read : — 

40691 ..r.r. 4123 

4074/ j;^ and 4137 

4076 *^^ 4149 

This last is followed by the line 4155 ; and between this and the 

4190 1 
broad band 4230 is a fine double 41 04 [ • 

These air-lines are present in nearly all the spark-spectra (scarcely 
recognizable in the spectra of Barium and Strontium). The metal- 
lines may commonly be distinguished by their different character — 
for example, the Bismuth-lines 4392, 4259, 4560, and 4722, in the 
second photograph of Pktte lU., and the Lead-lines 4058, 4246, 
and 4385, in the first spectrum of Plate XI. The substances to 
which the lines are due must be decided by internal evidence ; for 
there is no evidence given of the chemical purity of the metal em* 
ployed, and there is frequent evidence of impurity : for example, 
the Euthenium-spectrum is chiefiy due to iron. 

The value of the book would be much increased by a systematic 
identification of the lines — a work which the author does not seem 
to have very carefully attempted; at least he remarks that the 
Cadmium spark-spectrum is *' clear of air-lines," whereas the fact 
is that out of about 21 lines all but 2 are due to air. By such a 
systematic investigation, the spectra of many elements which have 
been pretty carefully investigated might be extended considerably 
towards the blue end with a certain amount of precision. 

Digitized by VjOOQIC 



Notices respecting New Books. 227 

The advantages of the photographic method are noticed by the 
author as follows : — "Absolute truth is everything in spectroscopic 
work ; and the very best draughtsman working vtdth the most per- 
fect micrometer cannot, even at the expense of a vast amount of 
labour, equal in accuracy a good photograph of a set of spectral 
lines." Of course the photographic plate cannot miss or make mis- 
takes in lines actually presented to it ; and Mr. Capron's work, as 
already remarked, is very useful as preliminary ; but the accuracy 
obtainable by measurement of his photographs is not as great as the 
author supposes. Indeed a greater degree of accuracy is attained 
by eye-measurements with a good micrometer. For measurement 
of the photographs, the reviewer has employed a photographic re- 
duction (on glass) of a millimetre-scale having about 5 divisions to 
a millimetre. For example, the wave-lengths of the Aluminium- 
lines obtained from an interpolation-curve drawn from the air-lines 
gave 5047, 4660, 4528, 4510, and 4476 ; Thal^n has for the same 
lines 5056, 4662, 4529, 4511, and 4476. And similar reductions 
of the iron-lines in the selenium-spark gave 4416, 4383, 4407, 
4323, 4304, 4268, 4257, 4248, 4148, 4072, 4066, and 4048, where 
Thal^n has 4415, 4383, 4404, 4325, 4307, 4271, 4260, 4251, 4143, 
4071, 4063, and 4045. With a similar direct-vision spectroscope, 
and the micrometer described in the Number of this Journal for 
August 1875, closer measurements can be obtained, as is seen by 
the following comparison : — 

Lines in the Spectrum of burning Magnesium. 
Direct- vision Six-prism automatic 

spectroscope. spectroscope. 

5006 5007 

4996 4997 

4985-5 4986 

4974-5 4975 

4963-5 4963 

4948-5 4948 

4934 4934 

Still very respectable results may be obtained by careful measure- 
ment of these photographs. 

There are several points of interest suggested by a study of these 
'* photographed spectra," — ^why, for example, some lines of par- 
ticular me&ls are plainly marked, while others are absent. For in- 
stance, in the Jj&sA spark-spectrum the line 4058 is sharp and 
bright, while there is no trace of the brighter line 4167. 

The photographs obtained from the electric light ore particularly 
interesting. Tins is, as far as we know, the first extensive series 
of measurements of spectra obtained by the ignition of substances 
in the electric arc. in all the photographs are seen, more or less 
distinctly, certain lines which Mr. Gapron terms ^' point-lines." A 
few of these are certainly Iron-lines ; out a particular set, employed 
by Mr. Capron as **arc" reference-lines, are certainly due to Carbon. 
jQiey are seen in the third photograph of Plate Y., and are the 

Q2 

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228 Notices respecting New Books, 

lines which constitute the group of the Carbon-spectrum de- 
scribed in this Journal, S. 4. vol. mviii. p. 249. They are known 
to be due to Carbon and not to any of its compounds, inasmuch as 
they are given by the spark of the induction-coil in C^bonic oxide 
at high pressure, or in vacuum-tubes enclosing Cyanogen or Naph- 
thaline; and evidence is given in the paper cited that they are 
caused by Carbon at a higher temperature than that required for 
the production of the ordinary spectrum. A curious point noted 
by Mr. Capron in connexion with these lines is, that they are 
scarcely seen in the spectrum of the arc between carbon poles, but 
are brought out prominently on the addition of a volatile metal. 
They are very well seen in the photograph of the Cadmium-spectrum; 
and (Sodium (which Mr. Capron does not appear to have tried) 
is still more active in bringing them out. If they are due to incan- 
descent carbon-t/apour, the existence of the vapour for a moment 
may be intelligible in view of the strong reducing-powers of 8odium 
and Cadmium. 

Other Worlds than Ours. By U, A. Pboctoe. Fourth Edition* 
Longmans and Co. 1878. 

The announcement of a fourth edition of ' Other Worlds than 
Ours ' is a guarantee of the estimation in which Mr. Proctor is 
held as a popular scientific writer, particularly on astronomical 
subjects. In the present work his fertile pen attains a more 
lofty theme, soars above the passive matenal of suns, planets, 
and stars, and seeks in primary and secondary systems the abodes 
of living and intelligent creatures : accordingly we find it interme- 
diate between an astronomical and biological treatise ; dealing on 
the one hand more with the conditions of life than with life itself, 
while on the other such astronomical facts only are presented to 
the reader as the author considered necessary to illustrate and sup- 
port his main subject. 

The conditions of life on the Earth is the first lesson in connexion 
with other worlds taught us by the Solar system ; the distribution 
of climates, the adaptability of various forms of life to each, the 
regions capable of supporting certain kinds of vegetable and animal 
existences while others are totally unfit for maintaining these par- 
ticular forms, are arguments used by the author in treating of those 
globes in the Solar system which, from astronomical and meteoro- 
logical considerations he regards as suitable habitations for inteUi- 
gent beings. 

The great reservoir of living force Mr. Proctor finds in the Sun, 
the central and ruling body of the system. The light, heat, actinism, 
magnetism, and other influences emanating from him are trans- 
mitted to the globes around him, which respond, as in the case of 
magnetism, to the disturbances set up in the ocean of light sur- 
rounding him. The remarkable connexion existing between those 
tumultuously rushing currents rending apart the luminous clouds 
constituting his photosphere, and the delicate vibrations of the 
magnetic needle on the earth, point to a bond of sympathy between 



Digitized by VjOOQIC 



Notices respecting New Books^ 229 

the two bodies, the enunciation of which is eloquently treated bj 
oar author ; and no less interestingly is the maintenance of these 
mighty forces presented to the reader in the chapter on Meteors 
and Comets, which strongly reminds us of Haidinger*s theory of 
the formation of the Solar system from the aggregation of " cosmical 
dust." 

In treating of the special object of his work, the author calls 
attention to the division of the orbs of the Solar system into two 
classes, those of the minor and major planets, those nearer and 
those further from the Sun ; . and he finds that among the nearer 
orbs the conditions of life obtain to the greatest extent, while among 
the four larger planets the conditions which he is able to detect are 
incompatible with life such as we find on our own planetary abode — 
but rather that the two which are most open to our scrutiny have 
formerly borne, and may still to a certain extent bear, the relation 
of suns to the systems of moons circulating around them, which he 
considers may in all probability be so constituted as to sustain life 
8 ich as we are acquainted with. 

Having expressed in the fullest manner his views of the habita- 
bility or otherwise of Solar orbs, Mr. Proctor passes on to consider 
the question, Are the multitude of Stars which surround us Suns 
Bimilar to our own ? In treating of these bodies he divides them 
also into two classes — one consisting of those in which the spectro- 
scope reveals the existence of elements familiar to dwellers on the 
Earth, the other of those which the author terms " minor stars,** 
and which he considers are situated among the lucid stars — the two 
classes, with the Nebulae, constituting one great system, the outer 
boundaries of which our most powerful telescopes are quite unable 
to reach. Eeasoning from the analogy of the Solar system, Mr. 
Proctor suggests that the larger stars, some of which are consider- 
ably larger than our sun, are surrounded by worlds of a similar 
character to our own. The following quotation, which closes the 
chapter on the Sun, embodies an epitome of his views : — 

*^ Lastly, turning from our sun to the other suns which shine in 
uncounted myriads throughout space, we see the same processes at 
work upon them all. Each star-sun has its coronal and its zodiacal 
disks formed by meteoric and cometic systems ; for otherwise each 
would quickly cease to be a sun. Each star-sun emits, no doubt, 
the same magnetic influences which give to the zodiacal light and to 
the solar corona their peculiar characteristics. Thus the worlds 
which circle around those orbs may resemble our own in all those 
relations which we refer to terrestrial magnetism, as well as in the 
circumstance that on them also there must be, as on our own earth, 
a continual downfall of minute meteors. In those worlds, per- 
chance, the magnetic compass directs the traveller over desert 
wastes and trackless oceans ; in their skies, the aurora displays its 
brilliant streamers ; while, amid the consteUations which deck their 
heavens, meteors sweep suddenly into view, and comets extend their 
vast length athwart the celestiid vault, a terror to millions, but a 
subject of study and research to the thoughtful." 



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280 Notices respecting Neto Books. 

A Treatise on the Stability of a given State of Motion, partieukuiy 
steady Motion; being the Essay to which the Adams Prize was 
adjudged in 1877, in the University of Cambridge, By E. J. BouTH, 
MA., F,R,S., Sfc. London : Macmillan and Co., 1877. (Svo. 
Pp. 108). 

The question, to which this Essay is an answer, was proposed in 
the following words : — " The Examiners give notice that the folr 
lowing is the subject of the Prize to be adjudged in 1877 : The 
Criterion of Dynamical Stability. To illustrate the meaning of the 
question, imagine a particle to slide down inside a smooth inclined 
cylinder along the lowest generating line, or to slide down outside 
along the highest generating line. In the former case a slight 
derangement of the motion would merely cause the particle to 
oscillate about the generating line, while in the latter case the 
particle would depart from the generating line altogether. The 
motion in the former case would be, in the sense of the question, 
stable, in the latter unstable. The criterion of the stability of the 
equilibrium of a system is, that its potential energy should be a 
minimum ; what is desired is a corresponding condition enabling us 
to decide when a dynamically possible motion of a system is such, 
that if slightly deranged, the motion shall continue to be only 
slightly departed from." 

In rery brief outline Mr. Eouth's answer to the question is as 
follows : — When a d3mamical syst^em is making small oscillations 
under the action of any forces which may or may not possess a 
force-function, and is subject to resistances which vary as the 
velocities of the parts resisted, the general equations of motion are 
linear ; and if A's=Me*"', &c. their solution depends on a determi- 
nantal equation 



/(m)= 



A, 13, O. • • 
A', B', C',.. 



=0, 



the constituents being all of the form A^A/n^+A^m-^A^; and if 
the system has n degrees of freedom, /(w) is of the order 2n. " If 
the roots of this equation are all unequal, the motion will be stAble 
if the real roots and the real parts of the imaginary roots are all 
negative or zero, and unstable if any one is positive. If several 
roots are equal, the motion will be stable if the real parts of those 
roots are negative and not very small, and unstable if they are 
negative and small, zero, or any positive quantity. But if, as often 
happens in dynamical problems, the terms which contain t as a 
factor are absent from the solution, the condition of stability is that 
the real roots and real parts of the imaginary roots of the subsidiary 
equation should be negative or zero.*' (P. 10.) 

When the system has two degrees of freedom the equation 
f(m):=0 is Ijiquadratic ; and this case has been worked out com- 
pletely in the third edition of the Author's treatise on Rigid Dy- 
namics (pp. 345, ). In the present case about a third of the 

Essay is devoted to a consideration of methods by which, \i-ithout 

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Geological Socitty. 231 

solving the equation, it can be determined whether the real roots 
and the real parts of the imaginary roots be negative. 

When the question has been treated thus far, a number of sub- 
sidiary points come under notice : ^. ^. in the case in which the 
system has a force-function, the equation /(m)sBO contains only 
even powers of m. This case also presents several points for discus- 
sion, such as the difference between oscillations about a position of 
equilibrium, and about a position of steady motion. Amongst other 
points which come up for discussion we will instance one more, to 
which a separate chapter is devoted, yiz. the question under what 
circumstances it is necessary to examine the terms of the second 
order in order to assure ourselves of the stability of the motion ; 
for it is possible that some of these may have their periods so timed 
that their effects accumulate until the character of the motion is 
changed. 

It is well known that, though it was intended to be given every 
alternate year, the Adams prize is but rarely awarded. We believe 
that on the occasion of Mr. Eouth's Essay the award was made for 
only the fifth time since the year 1848. This is a fact which 
Tenders any praise of ours superfluous. 



XXXIV. Proceedings of Learned Societies. 

GEOLOGICAL SOCIETY. 

December 5, 1877.— Prof. P. Martin Duncan, M.B., F.R.S., 
President, in the Chair. 

[Continued from p. 15S.] 

THE following communications were read : — 
3. ^On some Precambrian (Dimetian and Pebidian) Bocks 
in Caernarvonshire." By Henry Hisks, Esq., F.G.S. 

In this paper the author gave an account of the special examina- 
tion of the great ribs of so-called intrusive felspathic and quartz 
porphyries which are found associated with the Cambrian rocks in 
Caernarvonshire, made by him in company with Prof. Hughes, Mr. 
Hudleston, and Mr. Homfray last summer. He described sections 
at and near Moel Tr^-fan and across the mass from Pen-y-groes to 
* Talysaru, in which ho showed that instead of being of an intrusive 
nature, as hitherto supposed, tho whole, with the exception of a few 
dykes at those parts, is made up of bedded volcanic rocks, lavas, 
breccias, &c., similar to those found in the Pebidian series at St. 
David's, and that the Caml)rian rocks, instead of being intruded by 
this mass, rest everywhere upon it unconformably, and the pebbles 
in the conglomerate of the Cambrian at the base are, as at St. 
David's, identical with, and must have been derived from the rocks 
l>elow. Similar results were obtained in the examination to the 
north and south of Ll3'n Padarn ; and the conclusion, therefore, at 
which the author has arrived with regard to the great mass which 



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232 Geological Society: — 

extends firom Lkaellyfine in the south to St. Ann's chapel in the 
north is that it is entirely Precambrian, and that it belongs to the 
series described by him under the name Pebidian at St. David's. 

The other mass, extending from Caernarvon to Bangor, he con- 
sidered also entirely Precambrian ; and from the mineral characters 
exhibited by a portion of this mass directly behind Caernarvon, he 
thought it would prove to be, at least at this part, of Dimetian age. 
The altered beds near Bangor and their associated quartz felsites he 
considered entirely of Pebidian age, as there is no evidence that the 
Dimetian rocks are exposed there. 

4. " On the Precambrian Eocks of Bangor." By Prof. T. M^Kenny 
Hughes, M.A., F.G.S. 

The author described a series of slates, agglomerates, and por- 
phyritic rocks which, near Bangor, are seen to pass under the Cam- 
brian and seem to rest conformably upon the quartz felsites and 
granitoid rocks of Caernarvon. He thought that the Bangor beds 
were the equivalents of the felsitic and porphyritic series of Uyn 
Padarn ; and, in order to bring his interpretation into harmony with 
the observations of Prof. Ramsay, be explained away the apparent 
melting of the ends of the Cambrian beds in that section by twists, 
faults, and dykes. He referred the apparent unconformity recorded 
by Mr. Maw entirely to rock-structure, produced by cleavage on beds 
of different texture. 

He considered that in the main the Bangor beds were the equi- 
valents of the Pebidian of Dr. Hicks, while the Caernarvon beda 
nearly represented his Dimetian. But he thought there was as yet 
no proof of an unconformity between these formations. He would 
explain the apparent unconformity at St. David's by a continuation 
of bends and faults and joints mistaken for bedding, and would refer 
the brecciated rock of Low Moor, near St. David's, to the Pebidian, 
thus taking it on the wrong side of the supposed unconformity. He 
thought that the green be^ in the Dimetian were, in all the cases 
where he had been able to examine them, originally dykes. 

He saw, therefore, no reason from an examination of other areas 
to suspect any different explanation from that suggested by the ex- 
amination of the Bangor and Caernarvon district, viz. that we have 
in the Bangor and Caernarvon beds one great volcanic series, on 
which the Cambrian conglomerates and grits rest with a probable 
uncouformability. 

An appendix by Prof. Bonney on the microscopical examination of 
the rocks referred to accompanied this paper. 

December 19.— Prof. P. Martin Duncan, M.B., r.R.S., President, 
in the Chair. 

The following communications were road : — 

1, " On Argillornis longipennis^ Owen, a large bird of flight, from 
the Eocene Clay of Sheppey." By Prof. Owen, C.B., F.R.S., 
F.G.S., &o. 



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I 



Chronolfficcd Value of the Pleistocene Deposits of Devon, 233 

' 2. *^ GontributionB to the history of the Deer of the European 
Miooene and Pliocene Strata." By Prof. W. Boyd Bawkins, M.A., 

JF.R.S., r.G.s. 

3. " On the occurrence of Branchipus (or Chiroeephalus) in a 
fossil state, associated with Archceoniscus, and with numerous Insect- 
remains in the Eocene Freshwater Limestone of Gurnet Bay, Isle of 
Wight.'' By Henry Woodward, Esq., F.R.8., F.G.S. 

4. "The Chronological Value of the Pleistocene Deposits of 
Devon." By W. A. E. Ussher, Esq., F.G.8., of H,M. Geological 
Survey. 

In this paper the author endeavoured to work out the sequenos of 
events indicated by the Pleistocene deposits of Devonshire. He 
believed that during late Tertiary times subsidence extended to the 
south-western counties ; and to this he ascribed with some doubt 
the accumulation of a patch of gravel on the north summit of the 
Black Downs and of part of the old bone-breccia of Kent's Cavern. 
In the Glacial period, with the increase of cold, snow accumulated on 
the high lands, with formation of glaciers, which descended and 
united to form a great ice-field, planing the surface of a district 
composed chiefly of Cretaceous and probably Tertiary strata. To 
this period the author ascribed the formation of the clay with 
unworn fragments of flint and chert, and, doubtfully, part of the 
clays of the Bovey valley, the clay of Petrockstow, and part of the 
bone-breccia and the cr^'stalliue stalagmite of Kent's Cavern. The 
Postglacial phenomena he referred to three subperiods, in the first of 
which, during a gradual amelioration of the climate and disappear- 
ance of the ice, large quantities of surface-water were set free, 
redistributing and removing Tertiary outliers, partially destroy- 
ing the old ice-beds and moraine rubbish, and sweeping Secondary 
deposits from Palseozoic districts. The deposits then formed wcro 
supposed to be the old gravel patches of Colford and Orleigh Court, 
the waterworn materials on the Blackdowns and Haldon, the sands 
flanking the Bovey valley, and, with doubt, the redistributed 
Triassic pebble-beds of Straightway Hill, and part of the cave-earth 
of Kent's Cavern. The next subperiod he regarded as one of groat 
fluviatile action, the land being higher than at present, though 
sinking, and the meteorological conditions such as to greatly increase 
the volume of the rivers. The subsidence having continued to the 
level of the present raised beaches, reelevation took place, producing 
greater cold and more extreme seasons, and culminating in the 
production of continental conditions, permitting the southward mi- 
gration of a temperate fauna, and the advent of one requiring 
greater cold. During this period the gravels connected with the 
formation of the present valley-syst'Om, the raised beaches, and the 
" Head" were produced, and, doubtfully, part of the cave-earth and 
the granular stalagmite of Kent's Cavern, and the clay of Petrock- 
stow and Eoundswell. In the last subperiod the author considered 
that a subsidence took place, during which most of the valleys were 



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234 Geological Society: — 

excavated to their present depth, and forest-growth took plaee upon 
the old marine plain. The forests were then gradually circamseribed 
by the encroaching sea and diminishing rainfall, which also led to 
changes in the streams ; and finally the sea entombed the forests and 
swamps on the coasts, and produced the present diff-line. The 
results of this period are the submarine forests, most of the river- 
valley gravels^ and alluTial tracts bordering the preaeiit river- 
courses. 

January 9, 1878.— Prof. P. Martin Duneao, M3., F.It.S., 
President, in the Chair. 

The following communications were read : — 

1. *^0n the Great Flat Lode south of Kedruth and Camborne.'' 
By Dr. C. Le Neve Foster, B.A., F.G.S. 

The author described the mode of occurrence of the stanniferous 
deposit known as the Great Flat Lode, the mines worked in which 
extend for a distance of 3| miles, and furnish about ono eighth of 
all the tin raised in Cornwall. The mines in question are Wheal 
Uny, South Cam Brea, West Wheal Basset, South and West Whesl 
Frances, South Condurrow, and Wheal Grenville ; and in all the 
lode dips at a much less angle than the average of Cornish veins, 
the dip at Wheal Uny being only about 46° S. Throughout the 
lode contains a small leader, usually only a few inches wide, 
occupying the spaco due to the shifting of the two sides of a fissure, 
and filled partly mechanically, partly chemically. Above, or below, 
or on both sides of this there is a mass of stanniferous schorl rock 
from 4 to 15 feet wide; this contains from 1 to 3 per cent, of 
cassiterite, in little grains, or in strings or veins. Schorl rock, very 
■poor in tin (locally called capel or greybach\ separates the lode from 
the surrounding granite or kiUas, but passes on one side into the 
lode, and on the other into the granite or killas, so that no wall is 
recognizable. From these characters the author inferred that the 
lode and the capel are merely altered rocks, the fissure now occupied 
by the leader having served to bring up vapours or solutions which 
have entirely changed the rocks on both sides of it. In support of 
his opinion, the author adduced other instances of the change of 
both granite and killas into schorl rock ; and further stated that, 
both at South Condurrow and Wheal Grenville, he has found in the 
schorl rock cavities as large as a pea, agreeing in form with crystals 
of orthoclase felspar. 

2. " On some Tin-mines in the Parish of Wondron, ComwaU." 
By Dr. C. Le Neve Foster, B.A., F.G.S. 

*Tho mines described in this paper are called Balmynheer, The 
Lovell, and South Wendron. In the former the stanniferous de- 
posit consists of a large irregular mass of rock 30-50 feet thick ; its 
dip is N., at an angle of about 30°, and its strike E. 32? N., along 
which it has been traced for 36 fathoms. The tinny rock is sex>a- 
rated from the granite above by a slide or vein of white clay, with 



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On some of the Stochworls of CornwalU 235 

a little quartz and mica, about 6 inches thick, but passes insensibly 
into the granite below. At the LoveU Mine there are two lodes, north 
and south, the former striking from 37° to 45^ N. of E. and capping 
N,W. at an angle of about 70°, the latter running E. 48° N. and 
dipping N.N.W. about 60°, so that the two lodes unite in going east- 
ward and in depth. The lode is Eeparated on one or both sides from 
the adjoining granite by a rock loccJly known as ** cab," 6-12 inches 
thick, composed of quartz, mica, gilbertite, chlorite, iron-pyrites, 
copper-pyrites, and a little schorl. The lode itself shows joints which 
are mere planes of division in the roek, and usually have the same 
strike and dip. Divergent joints also occur ; and where these traverse 
the granite ^ey carry with them a little tin-stuflP for some distance. 
The South-Wendron Mine is worked in au irregularly cylindroid 
pipe of tinny rock, merging gradually on all sides into tiie granite ; 
the shorter axis of its oval section is about 10 feet, while the longer 
axis varies from 20 to 60 feet. It dips at an angle of 49° in a di- 
rection K. 25° W. The stanniferous rock in these mines is essen- 
tially a mixture of quartz, chlorite, gilbertite, iron-pyrites, and tin- 
ore, with zinc-blende in some cases, and usually some mica ; fine 
needles of tourmaline occur in the cavities which it encloses. In the 
South-Wendron Mine the southern part of the pipe is sometimes 
very granito-like in appearance, consisting of pink orthoclase crys- 
tals imbedded in a mass of quartz, chlorite, mica, and iron-pyrites, 
with a little copper-pyrites, fluor, and tin-ore. One specimen is a true 
stanniferous granite. These characters lead the author to the same 
conclusion he has arrived at in the case of the Great Flat Lode, 
namely that these tin deposits consist entirely of altered granite, and 
are not ordinary mineral veins : they have no walls, but the stannife- 
rous rock passes gradually into granite ; and they show no signs of 
banded structure due to the successive deposition of minerals. The 
highly granitic character of part of the South-Wendron tin deposit is 
strongly confirmatory of this view, which is further supported by the 
occurrence, in the dark mass of the so-called lode at the LoveU, of 
pseudomorphs of quartz after orthoclase containing a little cassiterite. 

3. " On some of the Stockworks of Cornwall." By Dr. C. Le 
Neve Foster, B.A., F.G.S. 

The author commenced by explaining that the term ^' Stockwork " 
had been derived from the German Sioclcwerck, meaning " Story- 
work," in allusion to the method of working in steps or stories 
in open workings, originally adopted for such deposits. Their being 
worked in open quarries affords a good opportunity of studying tho 
mode of occurrence of tin ; and many of them are interesting on 
account of the small percentage of tin which will cover all expenses. 
Thus, in the Wheal-Prosper Mine, the average amount of oxide of 
tin obtained per ton of stuff is not more than 3 lb., worth, at the 
present price of " black tin," 4^d. per lb. ; so that the ground as it 
stands is only worth ISJd. per ton. The mine can be worked 
without loss, on account of the softness of the rock and the large size 



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236 Grtologtcal Society. 

of the grains of tin-ore, the comparative lightness of the substances 
associated with it, and the command of water-power. 

The deposits worked as stockworks occur in Cornwall in killas, 
granite, and elvans. The tin-ore, associated with quartz and with 
small quantities of other minerals, is found in more or less parallel 
thin veins and strings, dipping at a high angle, and occasionally 
giving off branches or uniting with one another both in dip and 
strike. In the killas the rock close to the veins is oocasionaliy 
altered into tourmaline-schist; in the granite the walls of the veins, 
and sometimes the whole mass of granite, are altered into greisen 
and schorl rock. At Carclaze the orthodase of the intervening bands 
of granite has been converted into china-clay, which is now the main 
object of the working. At Carrigan the leader sometimes adheres 
to the enclosing rock by one side only, the other being bounded by 
a clay vein which contains broken cryst^ of cassiterite, indicating^ 
in the author's opinion, that a movement of the walls has taken 
place since the deposition of the tin-ore. Of the stockworks in 
elvans the author gave a list, and remarked that the elvan of the 
Terras Mine is particularly interesting, as it presents a series of 
cavities left by the removal of orthoclase, and now being filled up 
with schorl and a little oxide of tin. 

4. " The Precarboniferous Eocks of Cham wood Forest. — Part 11.** 
By the Kev. E. Hill, P.G.S., Fellow and Tutor, and the Rev. T. G. 
Bonney, F.G.S., Fellow and late Tutor of St. John's College, Cam- 
bridge. 

The authors described the result of the microscopic examination of 
a considerable eeries of the clastic rocks of Chamwood. Many of 
these, even among the finer beds, prove to be of pyroclastic origin. 
The coarser are generally composed of a groundmass of pulverized 
felspar, with viridite and some iron peroxide, full of larger frag- 
ments of felspar crystals (generally both of orthoclase and plagio- 
clase) and lapilli. The structure of these is often distinct, some are 
certainly andesites, others some kind of trachyte ; slaty fragments 
are also present, and occasional grains of quartz. The authors 
express their opinion that all the larger felspar crystals, and most, if 
not all, the quartz grains, are of clastic origin, even in the more 
highly altered varieties. Some of the larger fragments in the 
breccias were examined, and referred in part to devitrified trachytes 
not very rich in silica. The igneous rocks were then described. The 
syenites of the southern and northern districts were shown probably 
to belong to one system of intrusion. The homblendic granite of 
thoQuomdendi^^ct was also described, and the microscopic structure 
of the different varieties of it and the above investigated. A number 
of igneous rocks generally forming dykes in these was described : 
some appear to be altered basalts, others andesites ; one is a felsite, 
another a diorite. A group of outlying igneous rocks in the 
vicinity of Karborough was described. Of these, one is a quartz 
felsite with some hornblende ; another varies between this and a 



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Intelligence and Miscellaneoue Articles. 237 

qaartziforouB syenite ; the resfc are syenites ; and one contains so 
muoh plagioclase as to be almost a diorite. One of the aboTe, near 
Enderby, is seen to be distinctly intrusive in an altered slaty rock, 
which the authors have no doubt belongs to the Forest series. This 
discovery proves the igneous character of these rocks also, and 
extends the- area of the slaty series 6 miles further south than was 
previously known. A section was devoted to the faults of the Forest 
region. Here the principal fault runs along the anticlinal axb, 
with a downthrow on its eastern side which diminishes from 
2500 feet at the north end to 500 feet at the south end. East of this 
the beds seem undisturbed ; but on the west they are shattered by 
many faults, whose course cannot be traced. These are most 
numerous near Whitwick. The anticlinal fault is Precarboniferous. 
In conclusion, the age of the clastic and of the igneous rocks was 
discussed. The authors inclined to the opinion that the former are 
of the same age as the Borrowdale series of the Lake district 
(Lower Silurian), but admitted that the recent discovery of agglo- 
merates in the Precambrian rocks of Wales, and in the probably 
Precambrian ridges of the Wrekin district, weakens the argu- 
ments for this correlation. They do not think tbat there is any 
reason for supposing them Cambrian. If the Chamwood series 
is Lower Silurian, they think it most probable that the syenites and 
the Quomden granite were intruded in some part of the Old-Eed- 
Sandstone period, and that the later dykes were very probably 
Postccurboniferous but Prctriassic. 



XXXV. Intelligence and Miscellaneous Arttjcles, 

ON SOME MEASUREMENTS OF THE POLARIZATION OF THE LIGHT 
COMING FROM THE MOON AND FROM THE PLANET VENUS. BY 
THE EARL OF ROSSE^ F.R.S.* 

SEVEBAL years ago, at the suggestion of a friend, having ex- 
amined some portions of the lunar surface with a Nic-ols prism 
with a view to the detection of small sheets of standing water, if any 
such chanced to exist, I was led on to make a rather extended ex- 
amination of particular portions of the surface with the polarimeter, 
under the idea that if the precise position of elongation from the 
sun where the polarization of a point of the lunar surface attains a 
maximum could be accurately determined, it might be possible to 
obtain an approximate value of the refractive index of the material 
composing that surface, and so to distinguish between material of 
a vitreous nature, ejected from volcanoes, and a surface of ice and 
snow. 

The subject has been invested with the greater interest from 
the fact that Arago, having found the maximum of polarization 
of the whole of the moon's light to occur at or near quadrature, 

• From the Proceedings of the Royal Dublin Society, May 21, 1877. 
Communicated by the Author. 



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238 



IntelUt/ence and MUcellaneous Articles^ 



remarks on the circamRtance as being what might be expected to 
result from the reflecting surface being gaseous ; and he appears 
to think thafc the polarimeter may afford us some information on 
the question of the existence of a lunar atmosphere*. 

During the years 1872-75 we have at intervals made a rather 
extended series of measurements with the polarimeter, of which 
several different forms were tried, but one d^ering in little from 
Arago's was found the more satisfactory. 

Although from a series of sixteen readings of the inclination of 
the plates of parallel glass a value may be obtained for the polari- 
zation on each night w4th a probable error of observation not ex* 
ceeding 1 per cent., from some cause not yet estal^hed the dis- 
crepancies between the various nights' work are mneh larger, and 
the results must be accepted with reserve and regarded aa only 
provisional. 

The most probable values for the polarization (F), meaning by 
that term the proportion between the intensities of the components 
of the light polarized in and perpendicular to the plane passing 
through the sun at the several elongations (E), are for Maxe 
Crisium — 



£» 


p-1^ 


E« 


P.l-J- 


6^ 


0-830 


ii8 


0840 


70 


0-815 


120 


0-890 


80 


0-705 


130 


0-930 


90 


0-785 


140 


0-965 


100 


0-805 


150 


0-080 



Similar but less numerous measures than those on which the 
above table is based were made for Mare Imbrium, Mare Seieni- 
tatis, Palus Somnii, and the region between Macrobius and Proelns 
and other part-s. The polarization varies with the situation and 
with the nature of the surface, being in general greater on the 
plains than on the more uneven parts. 

Measurements of the light of the planet Yenus made between 
1872, March 12 and April 6, gave a mean value for the polarizatkm 
of 0*925, of which no regular variation was perceived during the 
progress of the observations, although the change of phase which 
occurred during the interval was considerable. 

May 16, 1877. 



QLASS-KNGRAVINa BY ELECTBICITY. BY M PLAlTTfe. 

I have previously described an experiment in which a glass tube, 
through which passes a platinum wire serving as electrode to a 
powerful galvanic current, was found to be instantaneously hollowed 
out in a conical or tunnel-«hape within a voltameter containing a 
saline solution. In other experiments, on the luminous effects pro- 

• Arago, (Euvres, nouv. 6d. par Barral, livr. xiv. chap. vL, t. iL p. 101 &c 



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Intelligence and Miscellaneous Articles. 239 

daced by a current of strong tension, at tho contact of the positive 
or negative electrode with the sides of a glass or rock-crystal vessel 
moistened with a solution of sea-salt, I observed that the glass or 
crystal was powerfully attacked at the points touched by the elec- 
trode, and that the concentric luminous rings formed around re- 
mained sometimes engraved at the surface of the glass of the volta- 
meter. On employing nitrate of potash as the valine solution, 
much less electric force was required, than with chloride of sodium, 
to produce these effects. 

These observations led me to apply the electric current to en- 
grave on glass or rock-crystal. The surface of a plate of glass or 
crystal is covered with a concentrated solution of nitrate of potass 
by simply pouring the liquid on the plate placed horizontally on a 
table or in a shallow basin. Next, a horizontal platinum wire, con- 
nected with the poles of a secondary battery of from 50 to 60 ele- 
ments, is immersed in the layer of liquid which covers the glass, 
along the edges of the plate ; then, holding in his hand the other 
electrode, consisting of a platinum Tiire enclosed, except at its ex- 
tremity, in an insulating sheath, the operator touches the glass, 
covered with the thin layer of saline solution, at the points where 
he wishes to engrave characters or a design. 

A luminous trail is produced wherever the electrode touches ; 
and whatever the rapidity with which one writes or draws, the 
strokes made are neatly engraved on the glass*. If the writing or 
drawing be done slowly, the strokes will be deeply engraved; their 
breadth will depend on the diameter of the wire serving as elec- 
trode ; if it is pointed, the strokes can be made extremely fine. 

The engraving can be executed with either of the electrodes ; but 
a less-powerful current is required for engraving with the negative. 

Although I have obtained those results by using seconda^ bat- 
teries, it is dear that, for continuous work, any other source of 
electricity can be employed in preference, if the quantity and ten- 
sion be sufficient— either a Bunsen pile of a sufticient number of 
elements, or a Gramme machine, or even a magneto-electric machine 
with currents alternately positive and negative. — Annates de Chimie 
et de Physiqwey Jan. 1878, tome xiii. pp. 143, 144. 



ON THX PHOTOMKTRIC COMPARISON OF LIGHT OF DIFFEREKT 
COLOURS. BY PROF. 0. N. ROOD, OF COLUMBIA COLLEGE, U.S.A. 
The comparison of the intensities of light of different colours 
has long been considered one of the most difficult of photometric 
problems ; but by the use of very simple means I have recently 
made a series of measurements of this character which may not be 
without interest to those whos3 studies lie in this direction. The 
luminosity of cardboard painted with vermilion was, for -example, 
measured as follows : — A circular disk of the vermilion cardboard 
was attached to the axis of a rotation-apparatus, smaller circular 

* There is po often occasion to write or to mark lines on glass in labo- 
ratories, that this process will there find frepent applications. 



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240 Intelligence and Miscellaneous Articles. 

disks of black and white cardboard being simultaneously j 
on the same axis, so that bj varying the relative proportio 
latter, a series of greys could be produced at will. 

The compound black-and-white disk was now arranged 
furnish by rotation a grey which was decidedly darker 
vermilion ; this grey tint was then gradually lightened till j 
server became doubtful as to the relative luminosities of 
and grey disks ; the angle occupied by the white sector ' 
measured. Next, a grey decidedly more luminous than thelj 
lion was compared with it, and diminished in brightness 
observer again became doubtful, when a second measurema 
taken. All this time the manipulation was performed by an] 
ant, the experimenter giving directions, but remaining in ig 
of the results to the end. The mean of ten such exp< 
assigned to the vermilion disk a luminosity of 23*8, that of 
cardboard being taken as 100. In this experiment and ini^ 
that follow, proper corrections were made for the amount of 1 
light reflected by the black disk, this having been previously f 
tained in a manner which will be described in a future con 
cation. 

In order to test the correctness of the final result, the lumil 
of a blue-green disk, correctly complementary in colour to 
milion, was next measured in the same way : it proved to be \ 
The vermilion and blue-green disks were then combined, accfl 
to Maxwell's method, so as to obtain a pure grey by rotatioi] 
the angular proportions of these coloured surfaces and the val 
the grey in terms of white and black cardboard measured, 
grey thus obtained had a luminosity of 24-54, that of white 
board being 100. Next, the value of this same grey was ( 
from the measured luminosities of the two coloured disks, anj 
proportions of these colours required to produce a pure |^ 
mixture on the rotation-apparatus ; the calculated value was i 

This agreement proves the correctness of the photometric < 
parison, and also of Grassman's assumption that the total inteii 
of the mixture of masses of difEerently coloured light is equfl 
the sum of the intensities of the separate components, which 
far as I know, has not before received an experimental confirmal 

Corresponding measurements were made with a green and 
complementary purple disk ; also with a blue and its complement 
yellow disk. The results are given below. 



Luminosity, 

Vermilion 23*8 

Blue-green 2^-5^ 



Obrome-yellow .... 80*3 

Cobalt-blue 35-38 

Green 41-19 

Purple 14-83 

-Silliman's American Journal, February 1878. 



Grey 
(observed). 

24-54 



54-51 
24-94 



Grey 
(calculated). 

25-47 
53-92 
26-26 



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Phil Ma^ S. 5. \fol. 5. 




a-& M* IV *v vm lU • 
Fig. 5. 



%■■*■ 



^' ^ i» U A /il 





«=' 



Mint«m Bros .Hih. 

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Phil. Mag S. 5. Vols 






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THE 
LONDON, EDINBURGH, and DUBLIN 

PHILOSOPHICAL MAGAZINE 

AND 

JOURNAL OF SCIENCE. 



[FIFTH SERIES.] 



APRIL 1878. 

XXXVI. Ea^perimenta on the Heat^onduetivity of Stone^ baaed 
on Fourier's * Thdorie de la Chaleur.' By W. E. Ayrtok 
and John Pkrrt, Pro/eseore in the Imperial College of 
Engineering^ TokiOy Japan*. 

[Plates IX. and X] 

L "11/ HEN a body is a good condactor for heat, it is compa* 
▼ ▼ ratively easy to find the conductivity correctly by the 
method employ^ by Principal Forbes, MM. Despretz, Wiede^ 
mann, Franz, and others, "which consisted in observing the tem- 
perature at different points of a long bar when one end had been 
Kept at a constant temperature sufficiently long for the tem- 

Ssrature of any one pomt of the bar to have become constant. 
ttt as the substances for experimenting on became less and 
less conducting, the amount of heat lost by radiation becomes 
larger and larger compared with that conducted along the 
bar ; so that this method of experimenting fails altogether for 
a non-conducting substance like stone. 

In such a case the plan usually adopted has been to measure 
the amount of heat conducted througn a very thin wide sheet 
of the material when the temperature of each of its surfaces 
was kept constant. But even wnen considerable precautions are 
taken to prevent loss of heat from the edges, &c. (such as those 
employed by Professor G. Forbes in his experiments published 
in the Proceedings of the Royal Society of Edinburgh for 
February 1873), still we feel sure that tibe results must be 

• Communicated by the Authors, having been read before the Asiatic 
Society of Japan, January 26, 1878. 

Phil Mag. S. 5. Vol. 5. No. 31. Apra 1878. R 

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242 Professors W. E. Ayrton and J. Perry on 

somewhat doubtful. We are not, therefore, surprised to find 
the conductivity of marble to be 0'0048 (gramme, centimetre, 
second) as given by M. P^clet in 1841, to be 0*0097 for fine- 
grained and 0*0077 for coarse-grained marble, as given by 
M. Despretz in 1853, and as 0*0017 as given by I^rof. G. 
Forbes m 1873. 

The method employed by Principal Forbes, and Sir W. 
Thomson, in 1860, of deducing the conductivity of rock from 
observations of underground temperature is, of course, sus- 
ceptible of much greater accuracy than the method referred 
to above ; but it has the disadvantage that a considerable period 
of time is necessary for the completion of one experiment, and 
it can only be performed on a rather large depth of rock form- 
ingjpart of the earth's crust. 

The following method which we have employed for deter- 
mining the conductivity of heat in stone, and which was 
suggested by some remarks made by Sir W. Thomson when 
lecturing to the Higher Natural-Philosophy Glass, in Glasgow, 
in 1874, has the great advantage of perfect certainty in the 
results ; and it can be used with comparatively little difiknilty 
for all bad conductors. The . principle consists simply in 
keeping a ball of the material to be experimented on in a 
water (or other) bath at a constant temperature for a sufficient 
length of time for the whole ball to acquire the temperature 
of the bath ; then suddenly removing the warm water and 
allowing a continuous rapid stream of cold water of constant 
temperature to flow round the outside of the ball, while time- 
readings of the temperature of some fixed point in the ball (for 
example, the centre) are taken as the ball slowly cools. Under 
these circumstances one of Fourier's well-known equations 
enables us to determine the internal conductivity of the ball, 
and the emissivity of the surface. 

The obvious difficulty in this method of experimenting is 
to determine the temperature, say, at the centre of the ball, at 
successive intervals of time, witiiout disturbing the flow of 
heat in the sphere. The comparatively small size of our balls 
of stone would make this difficulty very considerable if an 
ordinary thermometer were used; but those who have worked 
numerical illustrations of Fourier's results will see that the 
introduction into the ball of a th&rmometric junction attached 
to very fine leading wires cannot appreciably affect the general 
conditions. For absolute correctness it would be necessary 
to have a conical tubulure space of which the sides were coated 
with a substance impermeable to heat, extending from the 
surface of the ball to the centre, and terminating in a small 
spherical cavity at the centre, and to employ a thermometric 



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t/ie Heat'-conductivity of Stone* 243 

arraDgement of snch a nature as would not add to orsnbiract 
from th» heat at the centre. 

' One thermoelectric junction being at the centre of thebally 
the other may be either kept at a constant temperature, in 
which case the electric current will be a function of the dif- 
ference of temperature between the junctions, their mean 
temperature, the position of the neutral point for the two 
metals employed, and the slope of their thermoelectric lines ; 
or the other junction may be immersed in a compensating* bath, 
which, by being always kept at such a temperature that there 
ia no current, indicates at any moment the temperature of the 
centre of the ball. 

This latter, or balance, method was adopted, as it has the 
following advantages: first, the range of temperature through 
which the ball falls may be large, and still the galvanometer 
may be made as sensitive as we please ; second, the balance 
method may be employed nearly without reference to the 
'^ thermoelectric power of the two metals at different tern- 
peratures ; and, thirdly, since there is no current, no heat is 
added to or subtracted from the centre of the ball thermo- 
electrically, so that no vitiations of the theoretical conditions 
to ensure accuracy could occur except by heatKM)nductivity 
of the thin wires. In reality, of course, as it was impossible 
to cool the compensating-bath at exactly the same rate as the 
centre of the ball, there usually was a very weak current ; but 
as the junction in the bath was as often a very little hotter as 
a very little colder than that in the ball, the excessively small 
gains and losses of heat produced by the currents balanced 
one another. 

However, our balance method was employed chiefiy for the 
first two reasons, and not because we feared the abstraction 
of heat through thermo-electric currents. 

II. Details of the Apparatus. — In PI. IX. fig. 1, A is a stone 
ball 13-8 (thirteen and eight tenths) centims. in diameter, rest- 
ing on three points in a metal water-bath, B, 17*5 (seventeen 
and a half) centims. high and 18*3 (eighteen and three tenths) 
centims. in diameter. This bath had a tap, E, for letting in 
cold water of constant temperature from a cistern, and a large 
opening, O, which could be closed by a cork, for suddenly 
emptying B. The bath stood in a tub, W, to catch the over- 
flow, as will be described further on. At the centre of the 
stone ball there was a thermoelectric junction, C, of iron and 
copper, the wires being carefully insulated from the water and 
from one another except just at their extremities, where they 
were bound together and soldered, and immersed in a small 
drop of mercury to form good thermal contact with the stone. 

B2 

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244 Professors W. E. Ayrton and J. Perry on 

The cylindrical hole in the stone through which the wires were 
inserted was only made just large enough to receive them ; and 
the possibility of water entering the hole and making contact 
with the junction was prevented by the surface of we insu- 
lated wires being smeared over with a paste composed of white 
lead, red lead, and linseed-oil, which by hardening cemented 
the wires to the stone. The copper wire passed to a key, K, 
which was connected with one terminal, T, of a delicate dead- 
beat reflecting-galvanometer of about three quarters of an ohm 
resistance, whidi we had constructed for measuring thermal 
currents. The other end of the iron wire was bound and sol* 
dered at J to another copper wire, which was connected with 
the other terminal, T', of tne galvanometer. D D was a copper 
compensating water-bath, by means of which the thermo- 
electric junction J could be always kept at the same, or nearly 
at the same, temperature as the other junction at the centre of 
' the ball. To ensure the junction J quickly acquiring the tem- 
perature of the water in the bath D D, a small perforated platd 
of copper, P, was soldered to J and hung in the water with- 
out touching the sides or bottom of the bath. The bath was 
divided longitudinallv by a perforated copper plate, Q Q, to 
allow of the water bemg kept rapidly stirred (to ensure equa- 
lity of temperature) witEout risk of tiie Kew standard thermo^ 
meter S, which hung in the water, being broken. 

This bath was fittcS with two taps, U, V — ^the one for letting 
in cold water from the cistern, the other for emptying the bath. 
H is another thermometer hanging in the bath B, and having 
its bulb surrounded by a small metallic screen to shield it 
from direct radiation from the ball, but which allowed of free 
access of the water to the bulb. Either water-bath could be 
heated by suitable spirit-lamps. 

III. Method of eaperimentinff, — The two water-baths having 
been filled with water and left for a sufficiently long time for 
the temperature of all parts of the apparatus to have become 
uniform, or very nearly so, a reading of the galvanometer was 
taken, a small aeflection di being obtained. This deflection 
was due to a small unknown difference of temperature ti still 
remaining between the two junctions. The temperature of J 
was now raised by a number of small increments, ^, t^, &c., 
producing deflections d^, d^j &c. respectively ; then, since for 
small differences of temperature the currents are proportional 
to the differences, we have, if T is the difference of temperature 
corresponding with any small deflection D, 

+ ~3 — J + ■ 



T— rv dj—di d^—di d^ — d^ 

3 ' 

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the HeatHiOTkduciimty of Stone, 245 

the object of taking the mean of a number of observations 
being, of coarse, to calibrate the scale near the zero-point with 
considerable accuracy. This determination of the sensibility 
of the galvanometer was made before every experiment; and it 
was nsnally found that one division of the scale corresponded 
to rather less than one fiftieth of a degree Centigrade differ- 
ence of temperature between the junctions when the junctions 
themselves nad a temperature of about 23° C. This amount 
of delicacy was really more than was absolutely necessary, 
since the thermometer in the compensating-bath could only be 
read to the twentieth of a degree. 

The baths D D and B were now heated up to about 70° C, 
and kept at that temperature until the temperature of all parts 
of the stone ball had oecome uniform — that is, until there was 
no current when the two thermometers S and H indicated ex- 
actly the same temperature, the small scale-error in H 1>eing, 
of course, allowed for. At this moment the cork at was 
removed, the tap R opened, and a quantity of cold water poured 
into B by means of the tube M M so as to flood the bath B ; 
the whole of the warm water in B was therefore suddenly dis- 
placed by cold cistern-water. was now closed but K left 
open, so that there was a continual stream of cold water flow- 
ing upwards and overflowing the bath at the top. Constant 
readings of the thermometer in the compensating-bath, com- 
bined with simultaneous readings of the galvanometer (the 
latter being kept as small as possible), were now taken for about 
80 minutes, by which time the whole ball had cooled down 
nearlv to the temperature of the cold water. By opening the 
key K the zero of the galvanometer was frequently tak^n, to 
detect any slight change. It was the duty of one observer 
solely to observe the galvanometer, of another to cool the com- 
pensating-bath D D at the right rate and to take readings of 
the thermometer suspended in it, and of a third to record the 
time toffether with the readings made by the other two, as well 
as to taKe occasional readings of the thermometer H. 

IV. Reduction of the Readings, — Fourier's equation for the 
temperature of a point at a distance x centimetres from the 
centre of a homogeneous globe, when the globe has been 
initially all at constant temperature and when it is cooling by 
a constant external temperature being maintained, is 



«'°(%) 



2Er-, \ r) sina 



ttSK/ 



2\ ' / Dili » — --p /^x 



X /, sin2«\ 



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246 Professors W. B. Ayrton and J. Perry on 

where v is the exoess of temperatare of the point over iiie eix- 
temal temperatare on the Centigrade scale; 
vo is the excess of the initial temperatare over the ex- 
ternal temperatare; 
t is the time in seconds since the ball began to cool; 
r is the radius of the ball, in centimetres; 
E is the internal condnctivity, in centimetre-gramme- 
second nnits; 
E is the surface emissivity, which is such that from a 
square centimetre of surface 1 Centigrade degree 
higher than the external medium there will be emitted 
per second a quantity of heat E; 
C is the specific heat of the substance per unit volume; 
a is an angle such that 

Er » 
^""K^toiT^' (^^ 

from which equation successive values of a must be found and 
used to form the different terms under the sign of summation 
in equation (1). It is evident that the values of a will lie 
successively in alternate quadrants — the first, third, fifth, &c., 
or the second, fourth, sixth, &c., — also that after a certain time 
has elapsed, depending on the values of E, E, and r, all terms 
after the first become negligible, so that the true curve of v 
for a ffiven point becomes a simple logarithmic curve. 

If the point is at the centre of the ball, then, as ^ is nought, 

sin ( a - I 

a- 
r 

and the general equation becomes 

2Er ^ sin« -^* 

^v — ^) 

or, when all the terms except the first become negligible and 
therefore « is the smallest positive angle satisfying the equa- 
tion (2), we have 

2Er sina -^' 

Equation (4) may also be written In the forms 

, sin«— acosa _^^? ^ , 

t?=2vo = : e era /5) 

a— sm a cos a ^ ' 



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and 



tlie Heat-eonductivity of Stone. 
t?=N€-«', 



247 

. . (6) 

where N and m are supposed to be constant for the curve. 

Now it is easily seen that when K is considerable with regard 
to r^ as in ordinary balls of metal^ the period after which all 
other terms than the first are negligible is exceedingly short, 
and that this period is longer as the conductivity is less or the 
radius of the ball is greater ; and as we intend to use observa- 
tions made after this period, there is a certain size of ball for 
any given material which is most convenient for experiment, 
80 that it is of some importance to get a rough idea of the 
values of K and B before deciding on the size of the ball. 
From certain considerations of the possible errors in this me- 
thod of determining K, it will also be seen, further on, that it 
may sometimes be necessary to make two sets of experiments on 
a given material — ^the first to determine K roughly, the second 
with accuracy. 

Using the observations of which we have spoken, it is evident 

1 At? 
that -T—t which can easily be measured from the curve 

plotted from the observations, is m of equation (6), and that 
N may be determined from any observation, since 

N=i?€"'; 

so that if a time-curve has been drawn from the observations, 
m and N may be obtained from a very great number of points 
in the curve. Also vq is known ; ana 



Bin ae — a cos a 



N 



2a\ a— sin a cos a* 



(7) 



SO that a can be calculated. To calculate « when we know 
the value of this expression, a Table of the following kind will 
be found useful, in which it may be assumed that increase 
in the expressioir, for small increments, is proportional to a: — 



«, in degrees. 


«, in radians. 


sin«— acoBM 
«-Bin«eco8« 


114 59 
115-89 
120-00 
131-50 
14716 


1-9998 
20225 
20944 
2-2953 
2-5685 


0753 
0-738 
U757 
0-813 
0-893 



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248 ProfeBflors W. E. Ayrton and J. Perry on 

When a is knowni we can find K ; for 



*"=c?' 



or 



Also 



K 

Er 
K 






(8) 



= 1- 



tana 



so that E may be found. After the following illustrations of 
the method aescribed above, we shall consider the possible 
errors involved in calculating K and E in this way. 

V. As a first example, we shall take tiie time-curve of fall of 
temperature of the centre of a stone ball of 5^ centims. radius, 
which we obtained when the initial temperature of the whole 
ball was 70° 0., and the external temperature kept at 21°'3 C. 
during cooling. For reasons given further on, the first point 
we employ in the curve is when t equals 616 seconds from the 
commencement of cooling. The values of r, m, and logN 
corresponding with this and subsequent values of t are given 
in the following Table : — 



t 


«. 


m. 


logN. 





487 






616 


2579 


0-00178 


1-93656 


691 


22-46 


184 


194149 


766 


19-4 


206 


1-94216 


841 


16-62 


196 


1-94057 


916 


13-32 


209 


1-93867 


991 


12-3 


195 


1-93649 


1066 


10-66 


188 


1-93796 


1141 


9-2 


2U3 


1-93847 


1216 


7-9 


21)3 


1-93643 


1891 


6-77 


207 


1-93871 



In this case 



Mean«» ar 0'00197, 
Mean log N= 1-93825, 
MeanN =86-746. 



sin*— « cos « 
a— sin « COS* 



_ 86-746 

97-4 
=0-891 ; 



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ilie Heai'-conductwity of Stone. 249 

and we find from the Table given above that 

«=146°-76 ' /'. 

= 2*561 radians. /)> "^ /y 

Therefore K, which equals y >^ 

^2— > / /^" 

» I 

_ 0-00197 X 0-5738 x (5-5^ ^ V 

= 0-00520; 
and E, which equals — ( 1 — 1, 

=0-00464, 

the value of a obtained above being, as will be explained near 
the end of the paper, outside the limits within which small 
errors in K and E may be expected. 

Proceeding in a slightly different way, and determining 
each value of N from each separate value of m, and using the 
mean value of N as before, we find 
K=0-00518, 
E = 0-00502, 
the considerable difierence between this value of E and that 
obtained above illustrating what we say at the end of the paper 
regarding errors. 

The above observations were made very early in the inves- 
tigation, when we were not sufficiently impressed with the 
importance of keeping the external temperature really con- 
stant ; and hence the values of - -^ difier considerably at dif- 
ferent parts of the curve. We shall afterwards, however, give 
our reasons for believing that this does not much alter the 
value of K, although it seriously affects that of E. 

VI. In September 1876 we obtained the curve AAA, PL X. 
fig. 2, for the cooling of the centre of a stone ball 6-9 centims. 
radius, initially heated to 69°-62 C, the temperature of the 
stream of water flowing outside being carefully measured at 
every instant and plotted, giving the curve a a a, fig. 2, the 
scale for time in both curves being such that O X represents 
fifty minutes. To obtain K and E from these curves we em- 
ployed four different methods, as follows : — 

First method, — The external temperature having been plotted 
from the time when the curve for the internal temperature be- 
came logarithmic, the external-temperature curve was pro- 
duced until it cut the axis corresponding with time nought, 



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250 



Professors W- B. Ayrton and J. Perry en 



which it did at a point corresponding with 20^*1 C. His 
subtracted from 69^*62, the initial internal temperatare^ was 
taken to represent vq ; so that 

ro=49^-52: 
the yalnes of r were calculated by subtracting from each value 
of T (the internal temperature shown by the curve AAA) 
the corresponding value of a (the external temperature shown 
by the curve a a a). From the various values of ty the time, 
and of V the corresponding values of m and log N were calcu- 
lated; and the series of numbers obtained is shown in the fol- 
lowing Table : — 



t 


T. 


X. 


t;. 


m. 


logN. 


1050 


44-7 


19 


25-7 


0-001 io 


1-90014 


1200 


40-37 


18 69 


21 -68 


113 


1-80629 


1350 


367« 


18-38 


l8-;{8 


110 


1-89462 


1500 


33-68 


18 08 


15-60 


109 


1-89341 


1650 


3I»'98 


17-76 


13-22 


110 


1-89155 


IHOO 


28-75 


17 46 


11-29 


1(15 


1-br)304 


1950 


26-8 


17-15 


9-65 


104 


1-89491 


2100 


25-21 


16 9 


831 


(mo 


]-9<1002 


2250 


23-88 


1674 


7-14 


101 


1-90415 


2400 


22 73 


16 6 


6-13 


101 


1-9U793 


2550 


217 


16-5 


5-2 


109 


1-90650 


2700 


20-75 


16-4. 


4-35 


119 


1-89902 



Hence 



Meanm = 0-001075 
Mean log N= 1-89846 
MeanN =79-15. 



sina—otcosa 
a — sin a cos a 



2r, 



consequently 



whence 
and 



_ 7915 

99-04 
=0-7999; 

«=128°-62, 
or 2*2445 radians; 

K=0-00583, 



E= 0-00236. 

Second method. — As it is still an unsolved problem to find 
the general solution for loss of temperature in a globe when 
the external conditions are varying, the form of the functions 
being difierent from those employed in Fourier^s solution, we 



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the Heat-eondtLctivity of Stone. 251 

were led to make the assumption that if T^ 0. is the tempera- 
ture of the centre and ^° C. is the outside temperature at any 
instant, and if T^® C. was the initial temperature of the centre, 
then Fourier's equation becomes 



sma- 



or 



T-.^=2(To-^)^ 



•J^^^ rW, 



sin « cos « 



log (T-«) = log 2 + log (To-ar) + log 



sma—acosa 
a— sinacosoe 
Differentiating with respect to <, we have 



(9) 
t'Kt 



(V 



1 d 



1 dx 



T-xdt^'^ ^^~T^-xdt (V 



(V 



«»K 



from which ^-y, or w», can be found ; and when this is deter- 
mined we can find », since we can find from equation (9) the 
value of 

sina— «cosa 

; } 

« — Sin « cos a 

which ia called R in the following list of numbers, obtained 
from the curves AAA and a a a. 



t 


T. 


X, 


«i. 


B. 


•°. 


K. 


B. 





69-62 














1050 


4470 


1900 


000114 


0-840 


136-90 


0-00546 


000281 


12W) 


40-37 


18 69 


115 


0-846 


131-1 


541 


289 


1350 


36-76 


18-38 


114 


0-835 


1:^590 


553 


m 


15(NI 


33-68 


18-08 


113 


0^24 


133-7 


567 


265 


1650 


30-98 


17-76 


111 


0*795 


129-98 


608 


242 


]8(K) 


28 75 


1746 


108 


0756 


H9-79 


675 


220 


1950 


26-80 


1715 


106 


0-726 


113-33 


741 


199 


2100 


2521 


16-94 


104 


0700 


107-87 


793 


187 


S250 


23-88 


16-74 


105 


717 


111-44 


758 


194 


3400 


2273 


16-60 


108 


0-772 


12.M5 


63il 


223 


8550 


21-70 


16-50 


115 


0-919 


15236 


443 


249 



Mean K=0-00624. 

Mean E= 0-00237. 

Third method, — Assuming that the curve from 1050 seconds 
is logarithmic, and satisfies me equation 

where N and m are constants, and that the outside tempera- 
ture aP C. is constant but unknown^ we can find by the method 

of least squares the value of aP and of -%-, or m, in the 



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252 



Professors W. E. Ayrton and J. Perrj- an 



above equation. Choosing, for convenience, St equal to 150 
seconds, and patting 

__ Av_ 1 

we find from the curve AAA : — 



t. 


T. 


Equations. 


1125 


4253 


4-33j^+T=42-53 


1275 


3856 


3-61y+x=38-56 


1425 


35 22 


3-08y+*=35-22 


1575 


32-33 


270w+x=32 33 


1725 


29-86 


2-23y-hx=2»-86 


1875 


2777- 


l-95y+x=2777 


2025 


26-00 


l-59y+x=2600 


2175 


24-54 


l-33^+x=24-54 ! 


2325 


23 30 


l-15y4-*=23 30 


2475 


2221 


1 03 v+f=: 22-21 1 


2625 


21-22 


0'95y-^x=2\32 , 



Adding the above eqaations, we get 

23 95 y + lldr= 323-54. 

Maltiplying each eqaation by the coefficient of 1/ in it and 
adding, we find 

64-91 y + 23-95j:= 783-8; 

and from these two equations we find 

jr=15°-87 C, 

^= 0-1609, 



and therefore 



m or - $ =0-00107. 
V at 



These values of a and m were applied to every observation to 
determine N; and the values of log N so obtained are given 
below : — 

logN. 

1-9336 

1-9324 

1-9312 

1-9278 

1-9266 

1-9233 

1-9231 

1-9244 

1-9252 

1-9226 

1-9134 



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tlie ffeat-conductivitf/ of Stone. 258 

From these the mea^ valne of N was found to be 84*29 ; and 
since 

sing— g cos g __ N 

a — sin « cos a "" 2vq 

=0-784, 
it follows that 

« = 125°-54; 
so that 

K =1:0-00609, 
and 

E= 0-00226. 

Fourth method. — We now come to the last and most impor- 
tant method, to use which, however, requires a certain amount 
of experience in curves of this kind. If the stream of water 
outside the ball had been kept exactly at the lowest tempera- 
ture (16°-4 U.) all the time, then the centre would have cooled 
more quickly at the beginning, and the last observation would 
have been less than it is. A curve for the cooling of the centre 
when the external temperature is kept perfectly constant we 
shall call, for brevity, an exisothemiaX curve. We see there- 
fore that the exisothermal curve for 16°-4 C. will be altogether 
below the curve A A A, and the exisothermal curve for 19°-9 
will be below A A A for some distance at the beginning, and 
that it then cuts AAA and remains above it. 

If there are two exisothermals for the external temperatures 
Xx and x^ with the same initial temperature of the centre T, 

then, since at any moment — of the one equals — of the other, 

it follows, if P'' A and P'^B (fig. 3) are the exisotheimals in ques- 
tion, and if OA'' represents xi and OB'' represents or,, that 

AT _ B'Q 

^//p// - jj//p/7 ; 

so that if the point P is given and we want to find PQ, we 
have the equation 



PQ=(--,-^0(i-^). 



Now it w^ill be observed from this formula that all the exiso- 
thermal curves that we can draw from 19^-9 to 16°-4 C. almost 
coincide with one another for small values of the time, and 
even at 2700 seconds their distance asunder is not very great. 
With practice it is not difficult to see between what exbo- 
thermal curves lie the diiferent parts of the cun^e obtained 



Digitized by VjOOQIC 



»» 


1500 


99 


7> 


99 


18-69 „ 


ft 


2100 


99 


» 


W 


17-76 „ 


n 


2400 


» 


99 


» 


16-94 „ 


» 


2700 


99 


99 


^; 


16-6 „ 



254 Professors W. E. Ayrton and J. Perry on 

from the experiments. For example^ ^e carve AAA lies 
between the following exisothermals: — 

when ^=1200, between the exisothermals for lj9-3 and 18-69 

18-08 
1715 
16-60 
16-4. 

If this is true, then the ordinates of the cnrve A A A are 
greater than the ordinates of the exisothermal for 16°-4 C. by 
distances which are approximately slightly less than 

2-9(1 -^ -^ J) or 1-53 (say therefore equal to 1-50 for «= 1200), 

and slightly less than 

0-2(- 1 ^^) or 0-184 (say therefore equal to 0*18 for <= 2700). 

Consequently^ as in an exisothermal curve^ 

"* («,-<i)loge' 
it follows that in oar experiment m is very nearly equal to 
40-37 -16-4 -1-50 



and 



^'^g 20-75 -16-4 -018 ^^nno 



N=417€»7«»- 

=85-79 

N 

f-= 0-808} 

from which in the nsnal way it may be found that 
a =130»'47, 
K=0-00590, 
E= 0-00252. 

We see, therefore, that by these four methods of treating 
the curves AAA, aaa (fig. 2), which have been rendered 
necessary by the want of constimcy of the external tempera- 
ture, we have obtained the following results for K and £: — 



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the Heat-conduclimty of Stone. 



255 





iBt. 


2nd. 


3rd. 


4th. 


K 


0-00583 
0-00236 


0-00624 
0-00237 


0-00600 
0-00226 


0^00590 
0-00252 


B 





Now, as the present investigation was designed to show the 
feasibility of the experiments, and the possibility of deducing 
from them the numerical values of K and E^ rather than to 
obtain with the greatest possible accuracy the values of K and 
E for one particular Japanese stone, we have not thought it 
necessary before the publication of this paper to repeat the 
experiments, using greater precautions to ensure perfect uni- 
formity of the outside temperature by making the water-bath 
larger and the stream of cold water more rapid. And although, 
had we done so, any one of the above four methods w^ould 
have given results differing extremely little from the truth, still 
it would have been none uiq less interesting to have examined, 
as we have done, what method of reduction is calculated to 
give the most accurate results when there is a slight variation 
in the external temperature during the course of an experiment. 

Where considerable accuracy is required we should advise 
the employment of the fourth method ; if still greater accuracy 
b desired, then, several sets of observations having been made, 
the values of K and E should first be calculated by the fourth 
method; then, the mean of all the values of K having been 
taken as well as the mean of all the values of E, these results 
should be employed in drawing a number of exisothermal 
curves, when, lastly, the way in which the curves obtained 
from experiment lie among these exisothermals will enable us 
to calculate, again by the fourth method, the final values of K 
and E with any desired amount of accuracy. To illustrate 
this, we have drawn a number of exisothermals on the suppo- 
sition that 

K=p-00590, 

E= 0-00252; 

but the size of fig. 2, as engraved, only enables us to show 
two, B B B, C C C, the exisothermals for 16°-4 C. and 19°-3 C. 

From an examination of the way in which our curve A A A, 
obtained from the experiments, lies among these exisothermals, 
it will be seen that our first approximation is quite accurate 
enough for practical purposes, so that further approximations 
are unnecessary in this case unless very great accuracy be 
desired. 

VII. We made another series of experiments at the end 



Digitized by VjOOQIC 



256 Professors W. E. Ayrton and J. Perry on 

of September 1876, on the same stone ball of 6*9 (six and 
nine tenths) centims. radius, and fonnd that the fourth method, 
applied to the curve of falling temperature between 1050 
seconds and 2100 seconds, gave 

K= 0-00578, 

E=0-00263, 

We did not use the earlier part of the curiae, as we were de- 
sirous that all terms except the first should disappear in the 
calculations. The portion after 2100 seconds we also did not 
employ, as it is more difficult then to judge between what 
isothermals lies the curve obtained from the experiments. 

In the early part of September, 1876, we obtained the curve 
D D D, fig. 4, for the coohng of the centre of a stone ball of 5*5 
(five and a half) centims. radius, initially heated to 73°'62 C, 
represented by A, the temperature of the stream of water 
outside when plotted giving the curve dddj the scale of time 
in both curves being such that X represents 50 minutes. 
From these two curves, using the fourth method, we found that 

K= 0-00548, 

E =0-00495; 

on the assumption that the curve is within the exisothermal 
for 21^-5 C. at 450 seconds, and within the exisothermal for 
20°-2 C. at 1200 seconds. In the above calculations, although 
there is reason for believing that the stone, while of the same 
general character, differs somewhat in the two balls, we were 
compelled to use in both cases the same value of the specific 
heat (0*5738) per unit volume obtained experimentally from 
some fragments of the stone remaining after the turning. Our 
results obtained by the fourth method are therefore: — 



Badiufi of boll, 
in oentimetres. 


Initial tempera- 
ture, in degrees 
Centigrade. 


Outside tempe- 
rature at 2700 
seconds. 


K. 


£. 


6-9 
ti-9 
6-5 


69-69 
69-25 
73-62 


17-76 
17-9 


00(1590 
00573 
00(^48 


0^259 
0H>0263 
000495 



As we have only drawn attention to four curves obtained 
from the experiments, one in § V. and three in § VII., it may 
be as well to mention that several other curves were drawn 
from sets of observations made during July, August, and Sep* 
tember in the earlier part of the investigation. As, however. 



Digitized by VjOOQIC 



the Heat-conductivity of Stone. 257 

the special object of these earlier experiments was to familiarize 
ns with the method, we have not employed the results so ob- 
tained for the calculation of the conductivity. 

The considerable difference between the value of E obtained 
for the ball of 5^ centims. radius and for that of 6^^ centims. 
radius is due, to a certain extent, to the difference in the stone 
and difference in the surface, the smaller ball being of finer ^rain 
and having a smoother surface. The rock from which the balls 
were turned is a fine-grained variety of stone, which is largely 
used for building-purposes in many parts of Japan. Our 
colleague, Mr. J. Milne, Professor of Geology at this College, 
informs us that, with its varieties, it is a typical rock of tne 
country, forming in many districts large mountain-ranges. 
It is essentially lelspathic ; and the particular specimens em- 
ployed were, in the original state, probably a porphyritic tra- 
chyte, and, from the traces of hornblendic crystals which are 
apparently to be found in it, was also rhyolitic. Both the fel- 
spathic base and the enclosed crystals have been decomposed, 
especially the latter, which have been altogether kaolmized. 
Althougn the rock is generally light-coloured, it carries with 
it a slignt greenish tinge, due to the chloritization of a portion 
of the hornblende. The crystals of hornblende and the felspar 
are all of small dimensions, probably never more than two or 
three millimetres long; so tnat the specimens have as a mass 
a fine-grained homogeneous character. They also do not ap- 
pear to be at all calcareous. Owing to the nature of the pro- 
ducts of decomposition, the rock is soft and probably porous, 
and therefore to a certain extent permeable to water. 

VIII. We now pass to the consideration of the possible 
errors made in the determination of K and E by the method 
of experimenting that we have adopted. In the actual ther- 
mometer-readings there need not have been an error of more 
than 0°'05 C. ; but a single measurement of the actual tempe- 
rature of the centre of the stone ball may possibly have erred 
by as much as 0°*2 C, due to want of pertect equalization of 
temperature in the compensatin^-bath &c. As, nowever, the 
observations were all corrected by drawing time-curves, such 
errors were eliminated to an indefinite extent : and here it may 
be stated that regular curves were found to pass through 
nearly every point, as plotted from the observations on a large 
sheet of squared paper. 

Our methods of reduction being based on Fourier's mathe- 
matical calculations, really consist in finding exisothermal 
curves from the given observations. Suppose such an exiso- 
thermal curve found, then the value of v for any time t will 
be subject to an error which we may call 8r. Now it may be 

PhU. Mag. S. 5. Vol. 5. No. 31. April 1878. S 

Digitized by VjOOQIC 



258 Professors W. E. Ayrton and J. Perrj- on • 

easily shown that practically 

and we know from experience that there is no great error in 
the determination of m nnless the determination is made from 

very small values of v : consequently — is small. Again, 
since 






^=wi«— + — ; 



and as m is about O'OOl in our experiments, mt will be pracv 
tically between 1 and 3 for values of t between 1000 and 3OO0 
seconds; so that 

-«• is between 2 and 4 times — 

If we suppose the errors in the measurements of r and C (the 
radius and specific heat per unit volume) to be negligible^ we 
have for the error SK in K, arising from an error or in r and 
Svo in ^0, 

K wi a 

= 2 — approxmiately. 

But it may be easily shown that the error &t in « is such that 

S« _ /^ _ ^\ i5L (flt— sinacosflt)* 

"ii \ir t'o / 2^0 « sin«(a*^ + «8inacosa— 28in*«) 

/^ , .Bv Svo\ (sin « — g cos a)(« - sin a cos a) ^ . . 
= V^*^^7"i;^>'iisin«(«^nh«sin«cos«-2sin««)' ^^"^ 

gxr 
consequently it follows that the value of -w- will, as a rule, 

really depend on the value of the trigonometrical expression 
in equation (10). 

Similarly we may prove that 

SE _ 8m S« «^ 4- « sin gcos « — 2 sin^ a 
"F"" «r ^ sina(sin«— acosa) 



Digitized by VjOOQIC 



the HeaJL-conduciivity of Stone. 259 

therefore the value of SE will, as a rule, depend on the value 
of the trigonometrical expression in the last equation. Con* 
sequently we have calculated, as follows, the values of the tri- 
gonometrical expressions in equations (10) and (11) for 
different values of « :— 



«, in degrees. 


(sin «— « cos «X«— sin « cos «) 


«-8in«cos« 
Asin'a 


« sin « (•'-f« sin « COS • — 2 sin' «)' 


sS 


64 9«5 


0-67789 


30 


18-304 


0-69205 


50 


6-6181 


0-74277 


70 


3-5864 


0-83524 


!K) 


2-1975 


1-0023 


110 


1*5923 


1*3220 


130 


1-2369 


2K)740 


140 


11927 


29081 


150 


1*2356 


4-6616 


100 


1-4506 


9-5326 


170 


27473 


35078 


180 


QO 


00 



The curve A B, fig. 5, shows the scale of possible error in 
K for different values of a ; and the curve C D shows the scale 
of possible error in B. We see, therefore, that for given errors 
in t? and t?o the error in K is very great for small values of « ; 
so that, for instance, values of a less than 50^ are very unsnit^ 
able for use in calculations to determine K; and therefore, if we 
had used such a size of ball as gave a value of a less than 50^, 
we should have had to employ a new ball of more suitable size 
to get a more correct answer. There is a diminution in the 
possible error of K as a increases to about 140^ ; and from 160^ 
the possible error increases rapidly and becomes infinite when 
St = 180^* The error in B (the emissivity) is least for small 
values of a, and it increases with a, llius, to find K and B 
with errors of approximately the same amount, we ought 
to use such a size of ball as will make « about 120°. If K 
only is wanted accurately, we ou^ht to make a about 140° ; 
but if B only is wanted, then a £ouId be made as small as 
possible. 

We here append a list of accurately determined values of a, 

Br 
for different values of ^^ which Table, for reference further 

on, has been continued beyond a equals 180°:— 



S2 



Digitized by VjOOQIC 



260 



) Professors W. E. Ayrton and J. 


Perry on 


«, in 
degrees. 


radians. 


m 
tan« 


Er 


log "" . 
« — sin«008« 


18 


0174533 


0-989826 


0-010174 


1^927641 


20 


0-349066 


0-959051 


0-040949 


1-0920079 


80 


0-523599 


0-9069U0 


0-093100 


0-7419074 


40 


0-698132 


0-832001 


0167999 


4947749 


50 


0-872665 


0732253 


0-267747 


0-3041719 


60 


1047198 


0-604600 


0-895400 


0-1492815 


70 


1221731 


0-444674 


0-555326 


0-0185805 


80 


1-396263 


0-246199 


0-753801 


19051258 


90 


1-570796 





1*000000 


1-8048803 


100 


1-745329 


- 0307749 


1-307749 


17108789 


110 


1 919862 


- 0-698773 


1-698773 


T-6224941 


120 


2-094395 


- 1-209200 


2-209200 


T-5348553 


130 


2-268928 


- 1-903857 


2-903857 


1-4431355 


140 


2-443461 


- 2 912004 


8-912004 


T8408313 


150 


2-617994 


- 4-534490 


5-584490 


12145267 


160 


2792527 


- 7-672423 


8-672433 


1-0407430 


170 


2-967000 


-16-827080 


17-827030 


27430077 


180 
190 
200 
210 
220 
230 
240 


8141598 
3316126 
3-490659 
3665191 
3-839724 
4014257 
4-188790 


00 
18-806681 
9590509 
6-348295 
4-576005 
3-368360 
2418400 




2-7420334 
T-0330932 
T-1894748 
1-2833701 
T-3374829 
1-3628306 














250 
260 


4-363323 
4-537856 


1-588120 
0-800147 




T-8663971 
1-3531834 


0-199858 


270 


4-712389 





1-000000 


1-3267590 


280 


4-886922 


- 0-861696 


1-861696 


T-2893785 


290 


5-061455 


- 1-842220 


2842220 


T2419737 


300 


5-235988 


- 3-023000 


4-023000 


I-I840241 


310 


5-410521 


- 4-539861 


5539861 


T-1131865 


320 


5-585054 


- 6-656008 


7-656006 


T0243J54 


330 


5-759587 


- 9-975900 


10-975900 


2-9070970 


340 


5-934120 


-16-808865 


17303865 


2-7377888 


350 


6-108652 


-84-643888 


35-643888 


2-4417837 


860 
370 


6-283185 
6*457718 


00 
36-623589 




— • 
2-4412471 







Digitized by VjOOQIC 



the Heat^onductivity ofStone^ 
Table (continued). 



261 



«, in 
degrees. 


«,in 


tan« 


Er 


log ^- . 
«— sm«coB« 


380 
390 
400 
410 


6-632251 
6-806784 
6-981317 
7-155850 


18-221958 

11-789695 

8-820010 

6-004471 




27339632 
2-8945736 
2-9958956 
1-0605549 








420 
430 
440 
450 


7-330383 
7-504916 
7-679449 
7-853982 


4232199 
2-731566 
1-354095 





T0988471 
1-1166483 
11178020 
T-1049101 






1-000000 


460 


8-028515 


- 1-415644 


2-415644 


T-0795630 


470 


8-203047 


- 2-985665 


3-985665 


TK)423199 


480 


8-377580 


- 4-836798 


5-836798 


2-9925255 


490 


8-552113 


- 7176075 


8-176075 


2-9278685 


500 


8-726646 


-10-400014 


11-400014 


28433814 


510 


8-90n79 


-16-417294 


16-417294 


2-7288930 


520 


9-075712 


-24935814 


25-935314 


2-5620378 


530 


9-250245 


-62-460735 


53-460735 


22655615 


540 


9-424778 


« 




— <30 





In determining the most suitable size for our ball there are 
some other points to be considered: — 

First J for a given size of ball let us find the period after 
which the time-curve for v becomes a simple logarithmic curve 
— ^that is, the period after which 



sinai 



Cr» 



«! sin ai cos a^ 

is many times greater than 

sintf) 



a 2 -~~ 8m as cos as— 



e" era . 



Now for values of a such as we have been considering, the 
first trigonometrical coeflBcient is found to be two or more 
times the second, so that the second term will be negligible 
for a value of t such that, 



€" Cr* >100€" 






or 






Digitized by VjOOQIC 



262 Professors W. E. Ayrton- ar^ J. Perry on 

or 

•« "^^^KHogioc' 
It win be foand that 

aj— ajs20 approximately in all cases ; 

so that the above consideration reduces itself to 

.Cr»<10K^logio€, 
or 

^<4-343^ (12) 

For small valaes of a, such as we have not to consider in cal- 
culations of K, we use a different number from 2 in the ratio 
of inequality and we get different results. Notably we see 
that when a is very small^ as in Mr. McFarlane's experiments 
(described in Proc. Boy. Hoc. 1873), and in those on radiation 
in different gases at different pressures which we are at pre- 
sent carrying on, the second term in the series almost at once 
becomes insignificant. 

Second. Our next consideration, in connexion with the de- 
termination of the size of the ball, is to arrange that the fall 
of temperature shall not be too rapid ; otherwise it cannot be 
accurately measured, nor can the external temperature be kept 
constant. We may take it for granted that when v is, say, 50° 0., 
the fall of temperature should not exceed 1° C. in 15 seconds, 
or 

dv =1 

-^,ormt;, < j^; 

so that fTi, or p-^, must be equal to or less than 

T5750' "'• ^^^^- 

This condition, for different valu^ of a, becomes as follows: — 

o Cr* 

Ifa= 10, then -|^- must be equal to, or greater than, 22*904 



= 40, 


w 


;? 


w 


*> 


366-54 


= 80, 


V 


>; 


>> 


yy 


1465-9 


=110, 


yy 


yy 


« 


;^ 


2771-3 


= 120, 


yy 


>> 


;j 


jj 


3298-1 


=rl80. 


•y 


>? 


>j 


>; 


3870-9 


= 140, 


;> 


yy 


?> 


w 


4489-2 . 



u 



Digitized by VjOOQIC 



the Heat-'Condwctwity of Stone. 26S 

Now we have seen from the curves A B, C D (fig, 5), that 
the conditions of eaual and small errors in K and E necessitates 
a being about 120^; consequently conditions (13) require that 

-^ must be equal to, or greater than, 3298*1. But equation 

(12) requires that -^ should be less than 4*343^ ; 

.-. 4-343^mustbe > 8298-1, 
or 

^ must be > 759 seconds; . . (14) 

and this result is independent of the values of C, r, K, and £. 
If, however, it be desired to obtain the minimum possible error 
in K only, then the curve A B (fig. 5) shows us that a should 
be about 140^; therefore conditions (13) require that 

Cr* 

-^ should be equal to, or greater than, 4489'2. 

Combining this with equation (12), we see that 

4-343 1 must be > 4489*4, 
or 

t must be > 1034 seconds, 

a result also independent of the values of G, r, K, and E. 
Condition (14) is independent of the values of C, r, K, and 
E ; but substituting in equation (12) known values of C and 
K, we obtain a higher inferior limit for t. In our experiments, 
for example, 

0=0-5738, 
and 

K=: 0-006 about; 

so that for a ball' of 6*9 centims. radius, equation (12) leads 
to the result that 

t must be > 1072 seconds. 

If, again, we only wish that the possible error in E shall be a 

minimum, then a should be small ; consequently -^ may be 

small, and therefore t ; that is, we may use the curve from the 

beginning. 

Er 
We might here return to our Table of the Values of -^ ; 

and remembering that a must be about equal to 120 to give 
small and equal possible errors in K and E, we could deter- 
mine the size of the ball of given conductivity and emissivity 
most suitable for experiment. Thus we might show that, even 



Digitized by VjOOQIC 



264 Professors W, E. Ayrton and J. Perry on 

with the largest value of E which would allow ns with ran^ 
ning water to keep the ontside temperature approximately 
constant, the radius of an experimental ball to determine tfaie 
conductivity of copper would need to be greater than 500 oen- 
tims., and hence impracticable ; but if a more effective method 
could be emploved of keeping the outside temperature con- 
stant, then, makmg E, say, O'Ol, the radius of the copper ball, 
to give satisfactory results, ought to be between 50 and 400 
centims. It is quite evident, from such considerations, that 
our method of experimenting can only be used with substanoes 
having a heainjonductivity between 0*0003 and 0'03. 

At the commencement of our investi^tion we chose rather 
vaguely balls of 5*5 and 6*9 centims. radius, being guided only 
by former experience in numerical calculations under Sir W . 
lliomson, not having at the bemnning of our experiments 
worked out Fourier's formula, and being quite unable to obtain 
either Fourier's treatise De la ChaleuVy or any mathematical 
assistance in Japan. 

Now we see that in order that a should equal 120°, 

Er 

-^ should equal 2'21 ; 



that is, for the smaller ball, 
and for the larger. 



E 

jT should equal 0*4 ; 



E 

^ should equal 0*32: 

and we had reason to believe, as our investigation has since 

E 

proved to be correct, that ^ had about these values. If, how- 

E 
ever, we had found that ^^ was very different from 0*4, then 

we should have been compelled either to have made new stone 
balls, or to have varied E either by coating the surface of the 
ball, or by using, instead of the flowing water, the method of 
radiating to an enclosure. 

IX. As thi& is perhaps the first time that any series of ob- 
servations have been made illustrating Fourier's mathematical 
results, we think that students will be glad to get the obser- 
vations as they were obtained, without any correction whatever, 
from which the curves AAA, aaa (fig. 2) were drawn. 
They are as follows: — 



Digitized by VjOOQIC 



ilie Heat'Conductwity of Stone. 265 

September 25^ 1876. — Experiments on the atone ball of 6*9 
eentims. radiue. 

The galvanometer-Bcale having been calibrated, it was found 
that a deflection of one division on the scale to Uie right from 
the zero indicated that the junction at. the centre of the ball 
was cooler than that in the compensating-bath by 0*022 C. 
when the temperatures of the junctions was about 23° C. The 
ball was then Kept at 70° C. until the whole was at the same 
temperature* Tne hot water was then suddenly removed and 
a rapid stream of cold water at a temperature of 17° 0. allowed 
to flow over the ball, as described in § III. 





ObBeired 








Value of 






tempera- 


SsItaho- 


Ottlyftxio* 


Tempe- 


galvanome- 


True tem- 


Time, in 


ture of 


vnuTBUv 

meber- 
reading. 


meter 
aero. 


rature of 


ter deflec- 


perature of 


minates. 


compen- 
ntuig 


stream of 
water. 


tion in de- 
grees Cen- 


centre of 
baU. 




bath. 








tigrade. 







6§-8 0. 


5B 


. 


68 0. 


-O-IO. 


eh C. 


2 


70 


32 B 





23 


-0-7 


69-3 


2J 


69-2 


2L 







+0 


692 


3 


68-7 


8L 







+0-2 


68*9 


di 


68-6 


9L 







-fO-2 


68-8 


4 


687 


2L 





iV ' 





68-7 


^ 


68-6 


3B 







-0-1 


68-5 


5 


68-4 


2B 


2L 


•• • • 





68 4 


H 


68-6 


14B 


2L 


20-8 


-0-3 


68-3 


6 


681 


21 B 


2L 




-0-6 


67-6 


n 


67-2 


6B 








-0-1 


671 


66 


13 B 





26-8 


-03 


66-7 


8 


66-2 


48B 







-01 


65-2 


n 


66 


75B 








-16 


64-4 


681 


160L 





20-5 


+3-5 


61-6 


10 


58-6 


95L 







+20 


60-6 


m 


68-8 


43 L 





«•.... 


+ 10 


59*8 


11 


59-2 


20B 


IL 




-06 


587 


Ui 


59-3 


70 B 







-1-5 


678 


12 


58 


70 B 








-1-5 


56-5 


12i 


56 


32 B 





20-3 


-0-7 


55-3 


13 


55-2 


50 B 







-M 


541 


13i 


53*2 


22B 





■ •••• 


-0-5 


527 


14 


51-8 


lOB 





203 


-0-2 


51-6 


Ui 


51-4 


29B 







-0-6 


50-8 


15 


49 8 


5B 





,, 


-01 


497 


15^ 


49-4 


34 B 





20-3 


-06 


489 


16 


48 


15B 







-0-3 


477 


16* 


471 


20 B 





• •• 


-0-4 


467 


17 


45-7 


5B 





20-3 


-01 


45-6 


17i 


44 


29 L 







+0-6 


44-6 


18 


43-9 














43-9 


18* 


43-3 


15B 





20-3 


-03 


43 


19 


41-6 


21 L 





•••■•• 


+0-5 


421 


m 


411 


5L 





20-3 


+0-1 


41-2 


20 


40-2 


6L 







+0-1 


40-3 


21 


39-6 


33B 







-0-7 


38-9 



Digitized by VjOOQIC 



266 



On the Heat'-conduetwity of 3tone. 



Table {continued). 



Time, in 
minutai. 



Observed 
tempera- 
ture of 
compen- 
sating 
bath. 



21i 

9i 

22^ 

23 

23} 

24 

!** 
25 

2fiJ 

26 

27 

27J 

28 

29 

29} 

30 

30} 

31} 

32 

32, 

33^ 

35 

36 

37 

38 

39 

41 

42 

43 

44} 

46 

48 

50} 



Ghdrano- 
meter- 
reading. 



38 5 C. 

38 

368 

363 

356 

342 

341 

33 

32-9 

32-5 

32 

31-4 

311 

30-8 

29-2 

29-2 

286 

28-5 

278 

271 

26-8 

261 

247 

24-3 

237 



221 

217 

21-4 

209 

203 

20 

17-6 



Galvano- 
meter 
sero. 



17R 
23B 

6B 
lOR 

5B 
27 L 

8L 
28L 

10 L 
6L 
4L 

15 L 

5L 

8B 

29 L 

9L 

15L 

IL 

2L 

IIL 

5B 

6B 

15 L 

IIL 

14 L 

25 L 

6L 

16L 

22 L 

12 L 

13 L 
IIL 
75 B 

11 L 



Tempe- 
rature of 
stream of 
water. 








































Value of 
galvaaome- 
ter deflec- 
tion in de- 
grees Cen- 
tigrade. 



20 

18-5 

i's" 

18"" 

i7-8 

17-8 



17*8 

17-7 
17-i" 

17*" 

17 

17" 



True tem- 
perature of 
centre of 
balL 



-04 

-0 5 

-0-1 

-02 

-01 

+06 

-I-0-2 

-I- 0-6 

-f0 2 

-l-O-l 

+01. 

+03 

+0 1 

-0-2 

+0-6 

+0-2 

+0-3 




+0-2 
-01 
-01 
+0-3 
+0-2 
+0-3 
+0-5 
+01 
+0-3 
+0-5 
+0-3 
+0-3 
+0-2 
-1-6 
+02 



3§ I C. 

37-5 

867 

36-1 

35-5 

34-8 

313 

336 

331 

32-6 

321 

31 7 

31-2 

306 

29-8 

29-4 

28*9 

28-5 

27-8 

27-3 

267 

26 

25 

24-5 

24 

23*5 

231 

22-4 

22-2 

217 

21-2 

20-5 

18-4 

17-8 



To illustrate the mathematical results in connexion with the 
cooling of a globe, given by Fourier in his treatise De la 
Chaleur, we have drawn figures 6 and 7. A ball of 6*9 cen- 
tims. radius, having an internal conductivity 0*00590 (centim., 
second) and an emissivity 0*00252, is supposed to have been 
heated all to a uniform temperature and then kept in a stream 
of cold water at constant temperature. The exisothermal curves 
PAAA, PBBB, PCCC, PDDD, PEEE, PFFF 
(PL X. fi^. 6) represent respectively the time-fall of tempera- 
ture of pomts situated — 



Digitized by VjOOQIC 



Digitized by VjOOQIC 



FMMag.S.5.VQl.5.rJ 



Digitized 



byG00gl%„,^Bn-S 



On the Correction of the Compass in Iron Ships. 267 

at the centre of the ball, 

at one fifth of the radios from the centre, 

at two fifths yy yj ;y 

at three fifths ,, ^^ y, 

at four-fifths „ „ „ 

at five fifths „ „ „ — ^that is, 

at a point on the circumference. 

In this figure (6), P represents the initial excess of tempe- 
rature of the whole ball over that of the stream of water, and 
O Q, measured along the axis of time, represents 2500 seconds 
from the commencement of the cooling. 

ThecurvesGGG, HHH,III, JJJ,KKK,LLL,fig.7, 
represent respectively the distribution of temperature from 
the centre to the circumference of the ball at times 100, 500, 
1000, 1500, 2000, 2700 seconds from the commencement of 
the cooling, OT representing the initial difierence between 
the uniform temperature of the ball and the stream of water, 
and R, measured along the axis of distance from the centre 
of the ball, representing the radius. 

We have to thank three of our students, Messrs. Asano, 
Fujioka, and Nakano, for assistance rendered in the experi- 
ments, and three others, Messrs. Nakahara, Nobechi, and 
Oshima, for aid given us in the calculation of the Table of the 

values of t for different values of a. 

tana 

January 1878. 



XXXVII. On the Correction of the Compass in Iron Ships 
without use of a Fixed Mark. By Sir G. B. Airy, K.CB.y 
Astronomer Royal *. 

[Plate XL] 

I AM indebted to Sir William Thomson for the suggestion 
that the Compass in an Iron Ship might be corrected for 
the efiects of the Permanent or Polar Magnetism of the ship 
without use of a fixed mark. On considering the subject, the 
process here described quickly suggested itself. It is based 
upon the following assumptions : — 

That the effect of the Transient Induced Magnetism may be 
neglected. 

That by means of an auxiliary compass the ship's head 
may be kept steady on one bearing for a few minutes. 

That the magnitude of the actual directive force may be 
ascertained, in terms of any arbitrary scale (the most con- 
• Communicated bj the Author. 



Digitized by VjOOQIC 



268 On the Correction of the Compass in Iron Ships. 

venient expression will probably be, the square of the number 
of vibrations made in one minute of time), by the vibration, 
either of the compass-needle if very finely mounted, or by the 
vibration of a needle suspended by a silk fibre, the compass 
being removed during this observation. 

It is almost unnecessary to say that the apparent bearing 
of the ship's head as referred to the disturbed compass, or 
rather the bearing of the disturbed needle as referred to the 
head-and-stem line of the ship, is to be observed. 

The circle represented in the accompanying diagram, PL XL 
(which, in practice, ought to be made from an engraving, in 
order that a separate circle may be used for each separate cor- 
rection of compass) is to be conceived as attached to the ship^s 
deck, with the line H S parallel to the ship's keel. 

Then the operation proceeds as follows : — 

The ship's head is to be placed in three different azimuthal 
directions ; the most favourable will be three directions which 
very rudely divide the horizon into three not very unequal 
azimuths. In each direction, the magnitude of the actual 
directive force, and the bearing of the disturbed needle as re- 
ferred to the head-and-stem line, are to be observed. 

In the first observation, let A represent the magnitude 
and direction of the actual directive force ; in the second and 
third observations, let B and represent similar quanti- 
ties. Take the metallic T-square represented at the bottom 
of the diagram ; apply its graduated edge to the points B and 
C so that the numerations of the graduations touching B and 
C are equal (the scale of the graduations is unimportant, all 
that is required being that they be equal on the right side 
and on the left side), and draw a pencil along the fiducial ed^e 
of the transverse arm, thus describing the line be, be. Apply 
the graduated edge in like manner to the points A and C, and 
thus describe the line ac, ac, intersecting the former line at 
P. The same operation may be performed on A and B, de- 
scribing the line ab, ab; but it is not required, as that line 
will necessarily pass through the point P. 

Then OP represents in direction and in magnitude (on 
the same scale as A 0, B 0, C 0) the magnetic force which 
must be introduced for the correction of flie compass. For, 
it is a force which accompanies the ship in all its motions ; 
and its introduction, and its composition with the observed 
forces A 0, BO, CO, will produce the resultant directive 
forces A P, B P, C P ; which, from the nature of the geo- 
metrical process, are equal, and will represent the terrestrial 
directive force, equal in magnitude for the three positions of 
the ship. 



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Mr. S. P. Thompson on Permanent Plateau^ s Films. 269 

The actual operation of correction will be the following :— 

1. The lengtn of the correcting magnet mast be parallel to 
OP. If it is to be applied end-on, it most be in the line P. 
If it is to be applied broadside-on (which is preferable) draw 
the line m m through and at right angles to P : the centre 
of the magnet must be in that line. 

2. Join P C, and if necessary produce to Q. Draw 
O B parallel to P C. Then Q R is the angle through which 
the direction of the compass-needle is to be changed by the 
application of the correcting-magnet ; and the distance of that 
magnet is to be changed (always preserving its direction, as 
already described) till the compass-needle points in the direc- 
tion B 0. Instead of C, A or B might have been used in the 
same way. 



Royal Obaervatory, Ghreenwich, 
March 11, 1878. 



XXXVIII. On Permanent Plateau's Films. 
By SiLVAKUs P. Thompson, B.Sc. B.A.* 

1. rilHE film-figures, which occupy so large a part of the 
JL researches of Plateauf upon the Molecular Statics of 
Liquids, when prepared with the glyceric fluid prescribed by 
their discoverer, are of extreme fragility and of snort duration. 
With such a liquid films have been made which lasted ten, 
twelve, or even sixteen hours in the air, and from fifteen to 
thirty hours when protected by an external vessel of glass. In 
one instance J, where chloride of calcium had been added to 
the liquid, a duration exceeding fifty-four hours was observed. 
The average duration of the films, especially if they are to be 
exhibited to a number of persons, is more brief. 

No method hitherto described of producing these films in a 
more durable or permanent form has been quite satisfactory, 
though there have been several attempts. Of these the writer 
was not aware when he began the present investigation, though 
most of them are mentioned in the later chapters of Plateau's 
work already named. A brief enumeration of these attempts 
will therefore preface a description of the process now an- 
nounced for rendering the films permanent. 

2. M. Plateau has himself endeavoured§ to fix the film- 
figures by dipping the wire frames into solutions which eva- 

• Communicated by the Physical So3iety. 

t Statiqfie exp^mentale et th^oriqtie des liqiudes soumis aux setdes forces 
moUculaires. Par J. Plateau. Gand et Leipzic: 1873. 
t Plateau, op. cit. vol. i.p. 176, § 106. 
S Ibid, vol li. p. 119, § 311. 



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270 Mr. S. P. Thompson on Permanent Plateau's Films. 

poratC; leaving films of greater or less tenacity. He was 
unsaccessfol with collodion and with albumen. A solution of 
gutta-percha in bisulphide of carbon gave better results. The 
system of films upon a cubical frame of 2 centims. side was 
preserved for several months, but eventually fell to powder. 
The same substance refused to form a film upon a frame of 3 
centims. side. Glass, which in the single instance of the 
spherical film or bulb is so familiar, presents too many difii- 
culties to be applicable for the production of the film-figures. 

Schwartz* succeeded with much ingenuity in obtaining the 
anticlastic film-surface upon a skew quadrilateral frame whose 
sides were 3*5 centims. long, with gelatine. 

Prof. Machf imitated the system of films developed upon a 
tetrahedral firame with thin laminae of caoutchouc covering 
the sides, and drawn together when the air was exhausted 
from within. 

Better results have been yielded by viscous liquids which 
solidify at temperatures moderately low. 

M. Kottier, of Ghent, has obl^ned films of considerable 
dimensions with a mixture, suggested by Bottger in 1838 for 
blowing bubbles, consisting of 8 parts of resin (colophony) with 
1 of linseed oil, and fusing at 97^. But the fihns were always 
found after a few hours to have broken by contraction. 

Mach^ has obtained films upon a tetrahedral frame of 5 cen- 
tims. side dipped in fused resin. He has also obtained films 
from solutions of alkaline silicates which hardened on exposure 
to the air. 

M. Plateau§ has found a mixture of 5 parts of resin with 1 
part of gutta-percha superior to resin alone. A system of 
films upon a cubical frame of 5 centims. side, prepared by M. 
Donny, was preserved for two years, but ultimately fell into 
fragments. 

3. The author's first experiments were made with pure 
amber-coloured resin fused. The resulting filn^s were brittle 
and of irregular thickness. When 10 per cent, of turpentine 
was added, the liquid was too mobile at high temperatures to 
form films, and at low temperatures too stiff to form them re- 
gularly. 

A mixture of pure resin with Canada balsam was tried, 
with good results ; and a series of experiments followed, to 

* Plateau, op. cit vol. i. p. 233, § 141. 

t I>ie Gestaiten der Flussigkeiten, Prag. : 1872. See also Plateau, up. 
oil, vol. ii. p. 874, § 210 his, 

X Wiener akademischer Ataeiger, 1862, vol. xlvi. 2nd part, p. 125, 
" Ueber die Molecularwirkunff der Flosedgkeiten.*' 

§ Op, cit, vol. ii. p. 119, § 314. 



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Mr. S. P. Thompson on Permanent Plateau^ s Filim. 271 

ascertain the best proportions. When the mixtnre contained 
a less proportion of balsam than 35 per cent, the films were 
too brittle, and irregular in form. If it contained more than 
70 per cent, of balsam the films did not readily harden, and 
were not formed without difficulty. A mixture of 55 per cent, 
of resin with 45 of balsam, which fiised about 85°, gave good 
films, tough on cooling, but somewhat brittle. The mixture 
yielding the most satisfactory results contained 46 per cent, of 
resin and 54 of balsam. This mixture is sufficiently fused at 
80° to be workable, but yields the best films at 93° to 95°. 
At 105° films can be obtained; and they are thinner than those 
formed from the more viscid fluid at 95°. At 110° films are 
still obtainable; and they frequently exhibit chromatic pheno- 
mena, but usually burst before hardening. 

[The specimens exhibited to the Society are made with this 
mixture. They include a cubical frame of 2*5 centims. side, 
and a tetrahedral frame of 3*1 centims. side. Larger specimens 
have been obtained, however, though they generally show 
some imperfection of form. I have had a flat circular frame 
of 11 centims. diameter covered with a film of beautiful trans- 
parency. Brass wire appears better than iron for the frames.] 

The films made with the mixture described are remarkably 
tough, and if preserved from rough handling appear to be of 
indefinite durability. A number of frames holding films have 
been hanging for over two months unprotected upon the wall 
of the laboratory of the writer, and are still intact. Brass 
wire of 0*33 millim. in diameter has been employed for the 
construction of the frames. When a thicker wire is used, the 
films become irregular from the longer retention of heat by 
the wire, and the consequent earlier cooling of the central 
-portions of the films. 

As with the soap-films, so with those of resinous matter, 
success depends largely upon the purity of material employed. 
Dust and oily matters must be scrupulously excluded ; and 
the resin should be retained at a temperature near its boiling- 
point for some time, to purify it of more volatile matter, before 
die balsam is mixed with it. 

The most perfect films are obtained when the wire frames, 
after being dipped in the liquid, are removed to an air-batb» 
at the temperature of about 80°, in which they are left, and 
iihe whole is allowed slowly to cool. 

In proof of the toughness of the films, it may be mentioned 
that a recent flat film upon a circular frame of 4 centim. dia- 
meter of iron wire of 0*9 millim. gauge sustained, without 
breaking, the pressure of a cylindrical fifty-gramme weight, of 
24 milHrns. diameter, placed upon its centre. 



Digitized by VjOOQIC 



[ 272 ] 

XXXIX. On Grove's Gas-Battery. 
By Henry Fobster Morlby, M.A.^ JB.Sc* 

IT appears to me that the qaestion as to the mode of action 
or the well-known gas-battery has not yet been definitely 
settled. 

1. The discoverer says, " The chemical or catalytic action 
can onl^ be supposed to take place, with ordinary platina-foil, 
at the hne or water-mark where the liquid, gas, and platina 
meet " f . Nevertheless he showed that water containing oxygen 
in one tube and hydrogen gas in the other tube gave a conti- 
nuous current];. As regards exp. 29 in the last-quoted excel- 
lent paper (viz. the experiment in which, hydrogen being in 
one tube and nitrogen m the other and no oxygen being dis- 
solved in the liquid, hydrogen was found to appear in the 
nitrogen tube), as Mr. Grove does not say that there is a cur- 
rent, and as the presence of a current would contradict the 
conservation of energy, I am inclined to think that the effect 
is due to diffusion, and that it would occur whether the plati- 
nums were joined or not. 

2. Mr. Justice Grove says that the phenomenon does not take 
place when the nitrogen is absent and its place filled by the 
liquid ; and this is just what we should expect if the effect is 
due to diffusion. Mr. Grove thought it just possible that the 
hydrogen decomposed the water in its tube, combining with 
the oxygen, and that an equal amount of hydrogen was libe- 
rated in the other tube, oince the total amount of water is 
not changed, it is clear that such a decomposition could not be 
accompanied by a current. 

3. Nevertheless Dr. Schonbein said that pure water con- 
taining no oxygen in one tube and an aqueous solution of hy- 
drogen in the other gave a continuous current§. M. Gaugain 
makes the same assertion, but adds that he deprived his water 
of air by boiling ||. To boil water and then let it stand in the 
air is evidently not enough to deprive it of oxygen ; hence 
these anomalous results may be due to the water not having 
been absolutely free from oxygen. Such a current, as before 
stated, would contradict conservation of energy : indeed it has 
been shown by Mr. Grove that water absolutely free from 
oxygen in one tube and hydrogen gas in the other tube pro- 
duces no currentlT. 

* Commumcated by the Physical Society. 

t Phil. Mag. December 1842. See also Phil. Trans. 1848, p. 107. 

t Phil. Trans. 1843, exp. 28 &c 

§ PhiL Mag. March 1843. 

II CompUsBendmy February 25, 1867 ; Phil. Mag. June 1867. 

% PhiL Trans. 1843, ezp. 7 and elsewhere. 



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Mr. H. F. Morley on Grove's Gas-Battery, 273 

4. In one experiment Mr. Grove arranged his platinum 
plates, which I believe were platinized, in such a way as just 
to cat the surface of the liquid in the tubes: he got a strong 
current until the liquid rose above the platinum, when it be- 
came very weak. M. Gaugain says, and, I think, rightly, that 
this is due to the greater tnickness of liquid through which the 
gas must now pass in order to get at the platinum — when the 
platinum is partly exposed the film along the line of junction 
being extremely thin. 

5. M. Guugain made a cell in which the platinum plates 
were movable, and determined, by the method of opposition, 
the electromotive force when the plates were partly exposed; he 
then lowered them until they were wholly immersed, and de- 
termined the elftctromotive force immediately. In this experi- 
ment the current was only allowed to flow for a few seconds. 
He found that the two determinations were the same, and 
concluded that the action of the battery depends entirely upon 
dissolved gas. It is, however, open to any one to assert that 
the platinums, when lowered, retained minute bubbles of gas 
on tneir surface, and that thus there were still many points of 
contact of liquid, gas, and platinum. 

6. M. Gaugain, following Dr. Schonbein, asserts that " the 
oxygen serves simply to depolarize the positive wire," and 
" that its ftinction is that of sulphate of copper in Daniell's 
cell " — in other words, that, were it not for the opposition 
current developed by the freshly-deposited hydrogen, the cur- 
rent could be kept up indefinitely without the presence of 
oxygen. As I have before stated', I cannot conceive this state 
of things. 

I. In order to show that some, at all events, of the current 
in the gas-battery is due to dissolved gases, I made the follow- 
ing experiments in the laboratory of Professor Carey Foster: — 
A gas-couple with wholly submerged non-platinized platinum 
plates was charged by electrolysis and short-circuited for a 
week, after which the lengths of the columns of oxygen and 
hydrogen were read off by means of a telescope on different 
days, the couple being all the while short-circuited. A similar 
couple, from which the platinum plates were removed after it 
had been charged, was similarly treated. 

The barometer-reading was, of course, corrected for expan- 
sion, for the column of liquid below the gas, and for aqueous 
tension, the slight effect of sulphuric acid on the aqueous ten- 
sion being neglected. A correction was applied for the curved 
ends of the tubes, and the corrected lengths reduced to 0° C. 
760 millims. 

PhU. Mag. S. 5. Vol. 5. No. 31. April 1878. T 

Digitized by VjOOQIC 



274 Mr. H. F. Morley on Grove's Gas-Batiery. 

The result in niillimetres for the couple without platinum 
plates was: — 

Nov. 13. Dec 11. Jan. 9. 

Hydrogen 763 764 76-3 

Oxygen 49-9 49-7 49-7 

Practically the volume of the gas in these tubes was not 
altered by difiusion. 

For the tubes which contained the platinum plates the lengths 
were: — 

Nov. 13. Nov. 20. Dec. 11. Jan 9. 

Hydrogen 56-5 566 555 55-0 

„ calculated 56-6 56-4 55-75 54-9 
Oxygen 344 342 34-2 

The second line is calculated from the first bv least squares, 
on the assumption of a uniform decrease of nydrogen. The 
jgreatest error is ^ millim. ; and 1*7 millim. has disappeared. 
The oxygen seems to have been supplied by the air. 

II. On December 111 joined the plates through a galvano- 
meter of 6917 ohms resistance. The connexion through the 
galvanometer was made without previously breaking the cir- 
cuit ; yet a current was instantly shown ; after 19 nours the 
deflection was 20^ divisions. By comparison with a Daniell's 
cell whose electromotive force I assumed to be 1*1, 1 found that 
a deflection of 1 division indicated a current of *()0000000056 
electromagnetic unit. 

If we assume that the current in the short circuit is the 
same as that passing through the galvanometer, an assumption 
which later experiments show to be not far from the truth, we 
shall find that 8 cubic millims. of hydrogen per week would 
be required to keep up this current. Now 32 cubic millims. 
have actually disappeared per week. The difference may be 
partly due to the inaccuracy of the assumption just made, and 
partiy to the fact that some of the hydrogen combines with 
oxygen that has found its way from the air into the hydrogen- 
tube, the local currents thus produced not contributing to the 
main current. 

III. An experiment similar to I., in which, however, the 
gases were prepared chemically, and in which there was also a 
gas-couple whose plates were not joined by a wire. The lengths 
of gas, m millimetres, corrected as before, were: — 

For the couple with joined plates — 

Maya Oct. 4. Loss. Jokme lost, in 

•^ cubic cenUms. 

Hydrogen 146*1 136*0 10*1 2*87 

Oxygen 64 8 62*7 2*1 -60 



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Mr. H. F. Morley on Grove's Gas-Battery. 275 

For the coaple with unjoined plates — 

Maya Oct 4. W l^l^^^ 

Hydrogen 63-9 59-3 4-6 -90 

Oxygen 64-1 61-3 2-8 '44 

For the couple with no plates — 

Hydrogen 92-0 86-9 5-1 1-30 

Oxygen 90*0 85-4 4-6 -74 

In this case a good deal of gas seems to have been lost by dif- 
fosion. 

The ratio of hydrogen lost to oxygen lost in the three cases 
is 4*8, 2*1, and 1*8 respectively. If we assume that 1*8 is the 
ratio of the gases lost through diiiusion^ and that the loss of 
oxygen in the first two cases is due solely to this cause^ we 
shall find that 1*79 and '11 cubic centim. of hydrogen respec* 
tively still remain to be accounted for in the two cases. I 
attribute this loss to local currents in the second case, and 
partly to these but chiefly to the main current in the first 
case, most of the necessary oxygen being supplied by the air 
to the liquid. 

IV. If the hydrogen in a gas-couple with submerged plates 
be warmed by the hand, tlie current is increased ; and if it be 
cooled the current is diminished : indeed it is very sensitive 
to changes of temperature, and of pressure also ; and hence it 
is hardly possible to determine its strength with much accu- 
racy. The further any horizontal layer of liquid in the hy- 
drogen-tube is from the gas, the less hydrogen does it contain. 
Any expansion of the gas from heat or decrease of pressure 
brings a more saturated solution into contact with the immersed 
plate and the current increases, whereas contraction produces 
the opposite effect. 

V. when a cell has been recently charged by electrolysis 
the current is at first very strong ; but it soon falls off, and at 
h)st remains of nearly constant strength. This is because the 
water was at first saturated with the gas, but this gas being 
used up by the current takes some time to be restored by so- 
lution at the surface, and when equilibrium is attained the 
liquid round the plate will contain less dissolved gas the further 
it is from the surface. M. Gaugain attributed the falling-off 
in the strength of the current to the deposition of hydrogen 
on the positive plate ; there is no need, however, for any such 
supposition. 1 employed a battery in which the plates were 
wholly immersed ; and the final current varied with the depth 
of the top of the plate in the hydrogen-tube from the surface, 
and with the resistance in circuit, as the following Table 
shows : — 

T2 

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276 Mr. H. F. Morley on Grove's Gas-Battery. 



n. 


C. 


B. 


B. 


Conic. 


83 


S5 


240,000 


8,000 


25 


03 


39 


11,800 


450 


40 


83 


49 


1,600 


87 


41 


8 


203 


10,200 


2,070 


204 


75 


217 


200 


43 


219 


105 


201 


10.200 


2,050 


i98 


11 


81 


244.5410 


19.800 


81 





277 


10,200 


2,800 


224 





91 


234,500 


21,300 


89 



n is the distance between top of plate in hydrogen-tabe and 
surface of liquid in that tube, in millimetres; nssO means 
that the plate cuts the surface and rises about 1 millim. above 
it : the plate in the oxygen tube was always at the same dis« 
tance from the surface and was wholly immersed. C is the 
final strength of current, asuall^ several hours after introdu- 
cing resistance, given in deflections of the galvanometer, each 
of which is about '00000073 weber. R is the resistance in 

ohms ; and E is ttwu^* 

In the first place, it seems that the increase of current con- 
sequent on causing the platinum to cut the surface is too 
slight to oblige us to assume that a new force is thereby 
brought into action ; in other words, the whole of the current 
in the gas-battery is due to dissolved gas. 

I tried to express the relation between n, C, and E in a for- 
mula obtained theoretically. In this I had but little success ; 
but perhaps I may venture briefly to indicate the results: — 
Let absciss® represent depth 
below surface; ordinates quan- 
tity of hydrogen in solution at 
any lev4l, supposed uniform. 
Imagine a tube of uniform bore 
open to air at D and to hy- i" 
drogen at A. Suppose B C a uniform platinum rod, or rather 
an indefinite number of infinitely near equal platinum plates. 
Consider them to form equal branches of a divided circnit, and 
suppose the strength of current the same in each. 

Suppose the number of molecules of hydrogen ejected from 
any layer in a given time to be proportional to the total num- 
ber in that layer. Let Ug be the quantity of hydrogen in a 
layer at distance a: from A ; then, when equilibrium is attained, 
t^Ug-i is proportional to the number of molecules destroyed 
in that layer in a given time ; hence it is between A and B 
and between C and D, but it is constant between B and C; 
or the curve representing quantity of hydrogen is straight, 




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Mr. H. F. Morley on Grove's Gas-Batiery. ill 

except between B and C^ where it is conio. I assumed that 
there is no discontinniiy, and that the electromotive force is 

Eroportional to the mean quantify of hydrogen in any layer 
etween B and 0, or, what is the same thmg, to the total 
quantity between those limits, and that the current is propor- 
tional to the total quantity destroyed per second. Hence I 
deduced the formula 

a + na)C=6-(c + nrf)E; 

where a, 6, c, d are constants depending on the lengths BC, 
CD, on the rate of escape of gas at D &c. The layer A was 
assumed to be always saturated. In the actual experiment the 
shape of the plates was by no means regular ; and even had they 
been quite regular, the assumption that the whole of each ho- 
rizontal layer is a uniform solution is far from the truth. So 
I wrote the formula in a little more general form, 

(H-na)C=t + n^— (c + nd)E. 
If in this we put a= -0006, 6=244-5, £=-3-2, c=-00725, 
d= — -0000715, we get the last column (called " C calc") given 
above. We should expect the last two results to be higher than 
the calculated values, since no allowance has been made for 
the capillary film rising round the emerging platinum. How- 
ever, tne formula evidently cannot hold for depths much greater 
than 63, and it would become necessary to introduce terms 
varying as v? &o, 

V I. From the above Table it is clear that the electromotive 
force is not constant, as in ordinan' voltaic cells, but rises with 
the resistance. The same thing happens with ordinary gas- 
couples with platinized platinum. In one case, changing the 
external resistance from 46 to 10,000 only lowered the current 
from 423 to 157 ; in another case, changing resistance from 
10,000 to 190,000 lowered the current from 690 to 140. - 

When the resistance is suddenly increased the strength of 
current suddenly falls, but it rises, at first quickly and after- 
wards more slowly, to near its former value. For when the 
resistance is incr^ised the current falls by Ohm's law ; but it 
now uses up less gas, so that the gas accumulates in the liquid, 
and by so doing raises the electromotive force, and therefore 
the current ; and this continues until eouilibrium is attained. 

So when the resistance in circuit is diminished the current 
rises suddenly, but afterwards falls to near its former value. 
For the current rises by Ohm's law ; but the increased cur- 
rent uses up more gas, and so impoverishes the liquid sur« 
rounding the platinum, thereby diminishing the electromotive 
force, and the current falls. 

These observations seem fatal to the hypothesis that the 



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278 Mr. H. F. Morley on Grove's Ga9-Battery. 

action oocnre at the junction of liqaid, gas^ and platinnni', 
for the gas at that point remains of constant density, whateTer 
the resistance in circuit may be. 

y II. As an example of these views, an ordinary gas element 
with platinized plates was joined through a resistance of aboat 
10 ohmS; including a galvanometer. After about 1^ hour the 
galvanometer was deflected 195 divisions ; and after 19 hours 
tne deflection was 189. The gas-element was now slanted at 
an angle of 40°, the plates forming inclined planes ; the car- 
rent rose gradually, and after 2^ hours the deflection was 235, 
after 23^ hours it was 221. The element was now rotated 90°, 
so that the plates were vertical, but their long diameter was 
still inclined at 40° to the horizon ; the current rose instantly 
to 265, and after 4| hours the deflection was 262. 

When the plates form inclined planes the line of janction 
between liquid, gas, and platinum is not altered ; but the whole 
surface of the liquid is increased, and the submerged plate is 
brought nearer to it; hence the current is increased. In tiie 
last position an increased line of junction is added, and the cur- 
rent is still greater. 

VIII. The current produced by the ordinary gas elements 
which I used was always greater when the tubes contained 
but little gas than when they were full of gas, the ratio being, 
in three cases. If, 7, and 18. This is because the greater the 
distance between the surface of the liquid in the tubes and die 
air the purer will the solution of gas near that surface be. 
Perhaps also the greater length of the plate may enable it to 
catch gas that would otherwise escape: the internal resistance 
between the most active parts, those near the surface^ would 
be rather increased than aiminished. 

However, the cells are not at all regular in their action ; and 
this may be due to irregularities in the deposition of the finelv 
divided platinum on the plates. These irregularities do not 
afiect y II., since the tendency of the cell on that occasion was 
to become gradually weaker. 

IX. M. Gaugain found that the electromotive force of pla- 
tinum-wire electrodes partly exposed to the gas was not altered 
by submerging them. I have said why this does not appear 
to me conclusive (5). But I inverted the experiment : ignited 
wires were put several centimetres below tne surface of the 
gases ; the electromotive force was 102. They were tben 
raised so as to be only just submerged; the force was 134. 
They were tben thrust up into the gases, and the force was 136. 
A key connecting the wires through a galvanometer ^was 
pressed down until the needle had got to the end of its fir^ 
swing ; when the needle had come to rest the operation was 



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Mr. H. F. Morley on Grove's Gas-Battery. 279 

repeated ; and the mean of the two swings is the number given 
above. The resalt agrees with M. Gangain's experiment. 

X On another occasion I measured the electromotive force 
of wholly submerged wires in a gas-couple by connecting them 
to a condenser^ and afterward discharging the condenser 
through a galvanometer. The electromotive force of thick 
and thin platinum wires was the same ; but this was 15 times 
that of a wire of gold. Probably in the gas-couple; as else- 
where, platinum exerts some specific attraction on nydrogen* 

XI. M. Gaugain considers the falling-off in the strength of 
a gas*couple after short-circuiting to be due to the deposition 
of nydrogen on the positive wire, which hydrogen is produced 
by the decomposition of water by hydrogen ; and he says that 
when the electromotive force of a couple fell from 152 to 30, 
that of the hydrogen-wire fell 26, while an antagonistic force 
of 96 was developed by the wire in oxygen*. From other 
experiments of M. Gaugain, I infer that the potential of each 
wire was compared with that of a third wire plunged in the 
liquid between the two tubes of the couple. He does not di- 
stinctly say that the positive wire of the couple actually became 
negative to the third wire, though this may perhaps be inferred 
from the expression '^ antagonistic.^' I consider the loss of 
potential to oe due to the liquid near the wires becoming im- 
poverished of gas ; and even should the oxygen-wire become 
negative to the third wire, it may only show that the liquid in 
its neighbourhood contains less oxvgen than that surrounding 
the third wire. But since a little Wdrogen must have found 
its way into the oxvgen-tube, this nas a much better chance 
of becoming attecbed to the platinum when there is little 
oxygen near to use it up (that is, when a current is passing) 
than when the circuit has been broken and the wire is sur- 
rounded by a strong solution of oxygen. Using a gas-couple 
-with wholly submerged platinum wires, and comparing these 
with a third wire in ihe liquid between the tubes by means of 
a condenser periodically dislbharged through a galvanometer, 
I found in two different cases, a and &, just before short- 
circuiting: — a. 6. 

Hydrogen-wire 108 74 

Oxygen-wire 12 17 

120 91 

and in the same soon after breaking the circuit: — 

a. b. 

Hydrogen-wire 41 12 

Oxygen-wire _0 12 

41 24 

* Comptes Bendtis, 1867. 



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280 Mr. H. F. Morley on Grove's Gaa-Battery. 

In one case the oxygen-wire gave a negative deflection of 
about 1. 

I found that when I ignited a platinnm wire in a Bunsen's 
flame it acquired a positive potential of about 20, as if it had 
absorbed oxygen. In §§ I A., X.; and XI. the cell was com- 
posed of a couple of test-tubes inverted in a beaker of aci<i, 
and the wires were introduced by pushing them through a 
couple of narrow U-tubes, the shorter arms of which were 
inside the test-tubes. This arrangement made it very ea^' to 
change the wires. 

XII. The maximum polarization of a voltameter is scarcely, 
if at all, altered by diminution of pressure (Crova) ; and the 
same seems to hold for increased pressure. So also is the 
electromotive force of a freshly charged gas-couple — ^beiiig, in 
fact, little less than that maximum polarization. I conneded 
the terminals of a gas-couple with a condenser which could be 
discharged through a galvanometer ; I then developed gas by 
electrolysis for a few minutes, during which time the diflTerenoe 
of potential between tlie wires, whidi I will call E, was 189, 
the pressure being 77 centims. of mercury ; the battery was 
then cut out, and as soon as most of the bubbles, except those 
sticking to the wires, had risen, I found E = 60. The wires 
were now short-circuited until Es34, when the pressure was 
increased to 145 centims., after which thebatterj' was put on and 
E=:191 ; then the battery was cut out as before, and £ = 62; 
then the wires were short-circuited till Ess 37; then the 
pressure was reduced to 22 centims. ; then the battery was 

Kton, and E = 200; after cutting out the battery, E = 60. 
e initial electromotive force of the element is not aflPected 
by the length of time the battery is in circuit. 

The difference of potential between the terminals of the bat- 
tery was about 260, but was slowly rising during the experi- 
ment. When hydrogen is liberated from the surface of the 
wire, the platinum attracts as much of it as it can : this 
quantity seems not to vary with the pressure; I do not 
know why it should so vary; and it determines the maximum 
polarization. The slight increase of the polarization with 
pressure may perhaps be attributed to changes in the densiiv 
of the oxygen. 

XIII. A gas-couple charged M^th chemically prepared oxygen 
and hydrogen was short-circuited through a galvanometer of 123 
ohms resistance, and subjected to various pressures, the top of 
the wire in hydrogen being 5'7 centims. below the surface of the 
liquid in its tube, and that of the wire in oxygen being 5*4 
centims. below the surface. At a pressure of 76 centims., 
deflection 15. At a pressure of 144 centims. the deflection 



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On some Physical Points connected tritli the Telephone. 281 

ffradaally rose in 7 hours from 12 to 26. The hydrogen-wire 
oeing 2*1, and the oxygen wire 1*9 oentim. below the surface^ 
at a pressure of 76 the current is 38, 

„ „ 40 „ „ 20 after 6 hours, 
„ „ 16 „ „ 7i after 5 hours. 
Now pressure divided by current for the last three cases 
gives 2, 2, 2*2 respectively ; or the current is directly as the 

Pressure. In the last case 7^ seems to be somewhat too low ; 
ut this may be attributed to bubbles of oxygen, which under 
the low pressure were given off in the hydrogen tube. For 
the first two cases, pressure divided by current gives 5*1 and 
5*5 respectively. It is possible that at the end of the second 
experiment the current was very slowly rising: the further the 
wires are from the gas, the longer, of course, does it take for 
equilibrium to be attained. 

In this experiment the gases were introduced bv stopcocks 
into the upper parts of the branches of a U-tube, tne platinum 
wires were sealed into the lower parts of those branches, and 
the bend of the tube had a tail by which the pressure was ap- 
plied ; so that the gases were introduced without coming into 
contact with the wires. The same instrument, being at hand, 
was used in § XIL, where it is called a voltameter. 

If the action of the gas-couple depends entirely on solution, 
it is natural that the current should be proportional to the so- 
lubility of the hydrogen — ^that is, to the pressure. But if 
there is really any antagonistic force kept up by hydrogen 
attached to the positive wire, we should expect that this force 
would not be altered by pressure, and so the whole current 
could not be proportional to the pressure. I suppose that when , 
by inoreased pressure, the electromotive force becomes equal 
to the maximum polarization, ftirther increase of pressure would 
not alter the current. 

The Physical Laboratory^ 
University College, Londo 
December 1877. 

XL. On some Physical Points connected with tlie Telephone. 
By William Hknby Pkeece, Vice-President of the Society 
of Telegraph JEngineers, Memb. Inst. C.E., ^c* 

THE introduction of the speaking telephone, by Alexander 
Graham Bell, has supplied physicists with an instrument 
of research as well as with an instrument of practical utility. 
It is an apparatus which, for the examination of certain kinds 
of currents of electricity, is the most delicate that has yet been 
invented. Indeed it has rendered evident the presence of cur- 
• CommimicAted bv the Physical Society. 



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282 



Mr. W. H. Preece on some PkyMol Points 



rents whose existence, though suspected, have hitherto elodfid 
the grasp of the electrician ; in fact its yeiy delicacy has proved 
the greatest obstacle to its general adoption. 

I. The Telephone cis a Source of Electricity. 
Faraday showed that, when a dosed conductor is mored 
across the lines of force in a magnetic field, a current of elec- 
tricity is generated within that conductor whose strength is 
dependent upon the velocity of motion of the conductor and 
upon the intensity of the magnetic field. It is, in fact, pro- 
portional to the number of lines of force cut through per unit 
of time. And also, when lines of force are projected throngh 
a closed conductor, a current of electricity is generated in that 
conductor, whose strength depends upon the magnetic intensity 
of those lines of force, or upon their number per unit area. 
The direction of the current in each case is found by Lenz's 
law, viz. that the current produced tends to resist the motion 

f reducing it. The new principle that has been developed by 
Vofessor Graham Bell is that the form and duration of that 
current is dependent upon the rate and duration of the motion 
of the moving body or of those lines of force. 

Let N S, fig. 1, be a perma- 
nent magnet, and « 6 a fixed, 
closed, conducting ring of cop- 
per around one pole of that 
magnet. Let c be a movable 
iron armature. Now, if we 
regard any two lines of force 1 
radiating from the pole N, and 
nearly cutting the ring a 6, then, 
as we make c approach or recede 
from N, those lines of magnetic 
force will change their direction, 
taking up position 2 ; and with each change of direction they 
will cut the ring a b, and currents of electricity in different 
directions will circulate through a b according to the direction 
of motion of the lines of force ; and the rate of increase and 
decrease of magnetic intensity (or of the increment and decre- 
ment of the current) will vary directly with the rate of motion 
of the armature c to or from the pole N. Thus, if c be a disk 
of iron vibrating under the influence of sound, the excursions 
to and fro of any point of the disk, though very small (in fact 
they are so small that they can scarcely be detected by the 
most delicate means — so small that they have led Graham Bell 
to imagine that the vibrations are molecular), are nevertheless 
sufficient to produce that motion of the lines of force which 
results in currents. It is, however, a fundamental principle 




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connected with the Telephotie, 283 

in acoustics, that wherever there is soand there is always vi^ 

bration. Sonnd and vibration are concomitant and inseparable 

phenomena. The air cannot prodace sound unless it is thrown 

into vibration ; and the air itself cannot be thrown into vibra^- 

tion unless the mass of matter in contact with it vibrates also. 

The amplitudes of vibration of the particles of the air themselves 

have never been measured, though the length of a sound-wave 

(a very different quantity) is accurately known. Lord Bavleigh 

has shown that an amplitude of only ,^^A^^.v of a centimetre 

. 1 .!; 10000000 

IS sufncient to produce sonorous vibrations. But though the 

amplitude of the vibrations be so small they are rapid. Now 
this rate of motion is sufficient to bend in the same ratio the 
lines of force cutting a 6, and thereby to produce currents of 
electricity in the ring a b whose number depends on the num- 
ber of vibrations, and whose form and intensity depend on the 
rate and amplitude of motion of the disk c. These currents 
are alternate, and so rapid that no known instrument but the 
telephone indicates them ; but they are readilv shown by a 
Thomson's reflecting galvanometer when the disk is gently and 
slowly pressed in by the finger, — ^in one direction when the 
disk is pressed in, in the other direction when the disk is allowed 
to fly back. 

I nave failed hitherto to make even an approximate mea- 
surement of their minuteness. We have no known standard 
to compare them with : we can only trust to the ear ; and that 
instrument is not only deceptive but variable. They are cer- 
tainly less than J^ of an ordinary working current. 
Mr. R. S. Brouffh, of the Indian Government Telegraph De- 
partment, has calculated that the strongest current with which a 
telephone is at any moment worked does ^otexceedyQ^^o^o^o^ 
of the C. G. S. unit, or weber ; and Professor Pierce, of Boston, 
found that similar effects are produced with an electromotive 
force of less than > ^ of a volt •r DanielFs cell. Thus we 
have a source of electricitv competent to produce currents of 
microscopic strength, which vary in form, duration, and inten- 
sity with the motion of the body producing them. 

II. The Telephone as a Detector. Rg. 2. 

Let n 8, fig. 2, be a core of soft iron surrounded 
by a closed conductor afb^, through which currents 
flow. Now this core will become magnetized with 
an intensity dependent solely upon the intensity c^ 
of the current ; and the intensity of magnetism at 
any moment will be a function of the intensity 
of the current at that moment; so that if the 
current increase and decrease with a given ratio 



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284 Mr. W. H. Preece on smne Phydcal Points 

and at a given rate, the intensify of magnetiBm will increase 
and decrease with the same ratio and at the same rate. 
ThQ disk cf is elastic, but it is rigidly fixed «t its axis ; 
it being of iron, it is attracted at any moment with a force 
dependent upon the intensity of the magnetism of the core 
n 8j and being elastic, it recovers, or tends to recover, 
its normal position whenever this intensity of magnetism 
ceases or diminishes. Thus, if the magnetic intensity varies, 
the force of attraction varies, and the rate of motion of 
the disk varies in the same way* Hence the disk will record 
exactly the variations of the currents ; and as the correnis 
are the result of the variations of the vibrations of another 
disk, the one disk cf simply repeats exactly the vibrations 
of the other disk : thus sounds are reproduced. 

Though in the earlier instruments the coil surrounded a 
pole-piece of soft iron, this pole-piece has since been discarded, 
and tne coil surrounds the pole of the magnet itself. The 
efficacy of the instrument has been in no way impaired by this 
change; and it has the additional advantage of being perfectly 
reversible, the same instrument being used for speaking and 
for hearing. 

III. Workifig the Telephone. 

There is a remarkable difference in the power of different 
voices to work the telephone. Shouting is of no use. The 
intonation must be clear and the articulation distinct, and the 
style of conversation approach more the sing-son^. I have 
heard Mr. Willmot, one of the electricians of theFost Office, 
through resistances that have drowned all other voices. The 
vowel sounds always come out the best ; the palatal sounds 
c, g, jj k and y, the worst ; in fact, the latter sounds are fre- 
quently lost. The ear also requires a certain education ; and 
the power of hearing varies surprisingly with the different 
ears and with different people. Singing always comes through 
with remarkable distinctness; and the sounds of a wind-instru- 
ment — ^the comet or the bugle — ^are reproduced with startling 
force. A bugle sounded in London was heard distinctly over 
the lar^e Com Exchange of Basiugstoke by a thousand people. 
This arises from the regularity as well as increased amplitude 
of the sonorous vibrations, and consequently from the regu- 
larity, uniformity, and increased strength of the currents of 
electricity. 

IV. Improvements, 

Every one who has the means at his disposal has been en- 
deavouring to increase the power of this instrument. I should 
be sorry to enumerate the number of experiments I have 



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connected with tfie Telephone. 285 

tried, but all with vexatiotifl, disappointing, and dispiriting 
failare. 

One of the earliest efforts was made by Mr. Willmot, who 
hoped by increasing the namber of diaphragms, coils, and 
magnets acted upon simultaneously, and joining up all those 
coils in series, to obtain a resultant effect that would magnify 
the out-going currents; but the result showed that, while the 
apparatus acted all right, the effect of displacement of each 
diaphragm decreased with their number, and the ultimate 
effect was the same as with one diaphragm. Mr. Willmot's 
instrument, which was made early in October last, is on the 
table ; M. Trouv^, in Paris, seems to have been woiting on 
the same idea. 

Increasing or varying the size, form, and strength of the 
magnet has produced little or no apparent improvement; for 
the resultant effect in all cases remained apparently the same. 

The greatest effect is produced with a compound horseshoe 
magnet, which is indeed one of the earliest forms brought out 
by Mr. Bell. Here we have two coils, utilizing the maximum 
number of lines of force ; and the effects produced are certainly 
the finest I have yet experienced. At Southampton, on the 
14th inst., in a small office, Mr. Willmot's voice (he was in 
London) was heard distinctly by the seven or eignt persons 
who were in the room at the time. Though I have made one 
with the largest and most powerful magnet I could obtain, the 
result has been as disappointing as in the previous cases. The 
telephone has certainly been brought to this country by Mr. 
Bell in almost its perfect theoretical form ; he is still labouring 
to improve it; and I am sure we all wish him success, 

V. Applications. 

However small and however sudden the currents may be, 
the telephone records them with great accuracy ; no known 
form of galvanometer or galvanoscope will do so. 

It is admirably adapted for showing the currents of induc- 
tion set up in contiguous coils or contiguous spirals. If re- 
versals or intermittent currents be sent through one spiral 
while the other be gradually removed away, the rapidly dimi- 
nishing effect of increased distance is very evident ; indeed 
all the phenomena of magneto-electric induction are strikingly 
shown by its means. It is also admirably adapted as a detector 
in the bridge of a Wheatstone's balance to test short lengths of 
wire, and it will probably enable us to obtain a closer approxi- 
mation to equality than we have yet secured ; it also enables 
Qs to adjust condensers with great accuracy. 

M. Niaudet, of Paris, has shown how it can be utilized to 



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286 Mr. W. H. Preeoe on wme Physical Points 

detect the presence of extremely feeble currents from doabiAd 
soarces of electricity. If currents from the supposed source 
be rapidly sent throngh one wire of a doable-wonnd ooil, and 
a telephone be fixed on the other nmning parallel to it, then 
the telephone would give eyidence of their presence, whidi 
would be indiscernible on any other instruiflent. 

It is admirably adapted also for testing leaky insulators 
and supports. 

VI. Inferences and ResuUs. 

The telephone explodes the notion that iron takes time to 
magnetize and time to demagnetize. If time were occupied 
in magnetizing, notes would be changed or lost ; but they are 
not altered. The notion of time is due to the action of in- 
duction in coils producing reaction and eatra currents. This 
is proved by the insertion of an electro-magnet or of coils of 
wire in a telephonic circuit. While it is possible to speak 
through a cable 100 miles long laid out siraight in the sea, 
it is impossible to speak through 20 miles when coiled in a 
tank. 

Its delicacy has detected the presence of currents in wires 
contiguous to wires conveying currents^ which have always 
been suspected, but have been evident only on wires running 
side by side for several miles (say two hundred) on poles or 
in well insulated cables. In fact, the most delicate apparatus 
has hitherto failed to detect the presence of these currents by 
induction in short underground wires ; but the telephone re- 
sponds to these currents when the wires run parallel for only 
a few feet. Thus, between one floor and anouier floor, at the 
Greneral Post Office, it has been impossible to converse by 
means of the telephone through a wire, owing to the presence 
of these currents of induction from the innumerable working 
wires contiguous to it, and through some of the underground 
pipes of the streets of London sounds are inaudible when the 
wires are working. In fact, two small-sized gutta-percha 
wires, one foot long^ were lashed side by side by Mr. Marson ; 
and when battery currents were sent through one, induction 
currents were distinctiy heard on a telephone fixed on the 
other. Indeed this induction between wire and wire, has 
proved the most serious obstacle to the practical introduction 
of the instrument. But it is not altogether irremediable on 
underground wires ; it can be surmounted in three ways : — 

1. By increasing the intensity of the transmitted currents 
so as to overpower the currents of induction, and by reducing 
the sensitiveness of the receiving apparatus so as to make tlie 
instrumentinsensible to currentsof induction though responsive 
to telephonic currents. 



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connected tcith the Telephone. 287 

2. By screening the wire from the inflaence of indaction. 

3. By neutralizing the effects of indaction. 

1. Mr. Edison in America has partially succeeded in effects 
ing the first cure ; but his results, thougn promising, have not 
jet reached a practical point. 

2. I have overcome the second difficulty in a way that will 
now be described. 

Let 1, fig. 3, be a wire used for telephonic purposes, and 2 

Fig. 3. 



(i^ 




^ 



be an ordinary telegraphic wire contiguous to it. Let us re- 
gard 1 and 2 as symmetrical and contiguous particles of the 
two wires. If a current flow through 2 it will affect 1 induc- 
tively both statically and 'magnetically. Let us regard the 
static effect first. If the current flow away from us, then we 
may consider the particle 2 as charged positively ; lines of 
electric force will radiate all around it, and that line which 
passes through 1 will inductively charge that particle negatively. 
This influence being felt all along me wire, a current in the 
reverse direction to that in 2 will flow through 1. The reverse 
would occur if we assumed the primary current to flow in the 
other direction. Hence, an induced current will flow through 
1, whenever the current in 2 commences and whenever it 
ceases. Now, if we place between 1 and 2 a screen of metal, 
or other conducting matter^ in connexion with the earth, then 
the line of electric force, instead of passing through 1, will 
terminate at the screen. Hence, if we surround the wire 2 
with a covering or sheath of metal, or if we submerge it in 



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288 Mr. W. H. Preece on some Physical PoinU 

water, all effects of static indaction will cease between 1 and 
2. In water they are not entirely eliminated, for water is a 
very poor conductor ; but they are so reduced by its in- 
fluence, as my experiments between Manchester and Liverpool 
and between Dublin and Holyhead have shown, that, if tlie 
water or wet serving had been a perfect conductor, they woold 
have been removed as far as regards static induction. 

But we have to regard magnetic induction as well. Besides 
establishing a field of electric force around 2, a current flowing 
throhgh that wire establishes a magnetic field around it, whose 
lines of force are circles, and whose directions are at right 
angles to the lines of electric force. Let us regard that line 
of force cutting 1. Each time a current commences, and 
each time it ceases, in wire 2, a line of magnetic force cuts 
wire 1, and produces in that wire a current of induction in tiie 
same direction as that produced by static induction. Now, if 
we make the screen of iron, those lines of force terminate in 
the iron and wire 1 is freed. Hence, if we sheath the wire 1 
with iron, it is not only freed from the effects of static induc- 
tion by being surrounded by a conductor in contact with the 
earth, but it is shielded from the effects of magnetic indaction 
by its sheath of iron. Hence both effects of indaction are 
entirely removed. 

3. They can be neutralized by means of a return wire, osing 
this return wire instead of the earth. If 1 and 2, fig. 4, be 

Fig. 4 
►jf 



two wires running side by side, then the current set ap by 
induction from neighbouring wires, in one wire is neutralized 
by the currents set up in the other side. 

But this assumes either that the disturbing wires are at an 
infinite distance from 1 and 2, or that 1 and 2 are infinitely 
near each other. All attempts to use return wires on existing 

Soles, in cables, or in underground wires have utterly failed to 
o away with inductive disturbance ; but Mr. Bell has had a 
single gutta-percha wire carrying two conductors made which 
verv nearly fulfils the conditions and gives excellent resalts. 

The extreme delicacy of the instrument has introdaced a 
disturbance from another cause, viz, leakage. Wires on poles 
are supported by glass, porcelain, and earthenware insulators ; 
but the best support that was ever devised is but a poor in- 
sulator in wet weather. Currents escape over their surface 
from the wire they support ; and these leakage currents find 



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connected with tlie Telephone. 289 

their way into telephonic circuits. Hence a telephone circuit 
which may work well in dry fine weather will prove absolutely 
unworkable in wet weather. 

Another source of trouble arises from what are technically 
called ^^ bad earths." It is almost impossible to make a perfect 
connexion with the earth. There is always some resistance 
at that point ; so that if two wires terminate on the same earth- 
plate, the one being a working circuit and the other a telephone- 
circuit, some currents from the former are sure to pass through 
the latter and disturb the telephone. A return wire perfecfly 
cures this evil. 

There are other disturbing elements that are peculiar. 
Earth-currents, which are always present in the wires, produce 
a peculiar crackling noise, similar to that produced by a current 
from a single fluid battery such as a Smee or a Leclanch^, not 
unlike the rushing of broken water. This is due to the pola- 
rization of the earth-plate, as the sounds produced by a battery- 
current are due to the polarization of the negative plate. 
When auroras are present these earth-currents become very 
powerful, and the sounds are much intensified. The effects 
of thunderstorms are very peculiar : a flash of lightning, even 
though so distant as to be out of si^ht, will produce a sound ; 
and if it be near enough to be only sheet lightning, it produces, 
according to Dr. Channing, of rrovidence, a sound like the 
quenching of a drop of melted metal in water, or the sound of 
a distant rocket. Moreover he says that this sound is heard 
before the flash is seen, proving the existence of some induc- 
tive effect in the air prior to the actual discharge. The tele- 
phone thus becomes an admirable warning of the approach of 
a thunderstorm. 

Sometimes a peculiar wailing sound is heard, which an 
imaginative correspondent of mine likened to " the hungry 
cry of newly-hatched birds in a nest." I am inclined to think 
that it is due to the swinging of the wires across the magnetic 
lines of force of the earth. It is not difficult to conceive that 
these vibrations may succeed each other in the necessary 
rhythmic order to produce musical tones. 

The wires are never free from sound ; and every change of 
temperature or of the electric condition of the atmosphere is 
recorded on this delicate apparatus. 

The expansion of the iron diaphragm under the influence 
of the warm and damp breath when the telephone is first raised 
to the lips preparatory to talk is very marked ; it produces a 
faint rustling shiver. 

Immediately on the introduction of the instrument, great 
anxiety was felt to learn its performance on submarine cables. 

PhU. Mag. S. 5. Vol. 5. No. 31. April 1878. U 

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290 Mr. W. H. Preece on some Phyncal Points 

A telephone was sent to Gaemsey, and Mr. Willmot went to 
Dartmouth, those two places being connected by a cable 60 
miles long. Conyersation was carried on, the articalation 
being perfect though slightly maffled. This was a surprise ; 
for it was felt that the static induction of a cable, by its retard- 
ing influence, would have prevented articulation by lengthening 
the waves of electricity and rolling them up as it were. 
Through the kindness of Messrs. Latimer Claik, Muirhead, 
and Co. I was able to repeat these experiments on an artificial 
Atlantic cable, constructed to duplex the direct United-States 
cable. With Mr. Willmot at one end and myself at the other, 
there was no diffical^ in speaking up to 100 miles, though 
the muffling effect or induction was evident. Beyond this 
distance up to 150 miles muffling commenced to seriously 
impede conversation, and the sounds diminished considerably 
in strength : it was like talking through a thick respirator. 
The effect diminished rapidly up to 200 miles, beyond which 
articulation became impossible, though singing was distinctiv 
heard ; indeed singing was heard through the whole length 
of the cable, 3000 miles long ; but this was traced to a secondary 
cause, it being due to the induction of condenser on condenser. 
Nevertheless there is no doubt that singing can be heard 
through a much greater length than speaking, due to the 
greater regularity of the successive waves of electricity. 

I subsequently experimented on the underground wires be- 
tween Manchester and Liverpool, a distance of about 30 miles ; 
and through this length we had no difficulty whatever in 
speaking. Again, between Dublin and Holyhead, through the 
cable 67 miles long, we spoke with ease, singing coming 
through with remarkable power and effect. This cable con- 
tains 7 distinct conductors. When one wire was used for the 
telephone, the sounds could be heard on every other wire, bat 
in a feebler degree. When the other wires were working with 
the ordinary telegraphic apparatus, induction was evident, but 
not sufficiently intense to stop conversation. Each wire would 
be surrounded with a wet serving of hemp ; but this was not 
of sufficient conducting-power to entirely screen the effect of 
induction. The same effect was experienced between Man- 
chester and Liverpool, where the wires are made up into 
cables of 7 conductors served outside with tarred hemp. 

The conclusion that I have come to is, that conversation 
mi^ht be held through a single wire cable 200 miles long 
with the apparatus that we now have ; what new apparatus 
will do no man is rash enough to predict. 

The reason for this surprising result is not difficult to 
explain : — 



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connected with the Telephone. 291 

Let the disk d, fig. 5^ be impressed forwards by a sonorous 
vibration^ it will generate in the coil c a positive carrent. 

Fig. 6. 





which, flowing through the line, will pass through the coil </ 
and attract the disk a. Now the effect of induction is to re* 
tard or prolong the effect of the positive current 1 ; but the 
motion of the disk dl has itself produced a current in the re- 
verse direction to the first current ; and this neutralizes the 
prolongation due to induction, and so helps to clear the line 
for the next signal, which passes through precisely the same 
process ; and hence the vibrations of the second disk tend to 
produce currents which diminish materially the effects of induc- 
tion, and so render possible conversation to distances that &r 
exceed anticipation. 

The extreme delicacy of Bell's apparatus has been shown in 
various ways ; for instance : — 

Extract from a letter from T. A. Edison, dated November • 
25, 1877. 

" I made a pair of telephones that work with copper dia- 
phragms : it IS on the revolving-copper-disk principle of 
Arago, 

"I find that a copper diaphragm may replace the iron in 
Bell's. Copper must be ^ in. thick. It is very low with copper 
in both ; but if the receiver is one of the regular kind, and the 
transmitter is a copper diaphragm, you can carry on conver- 
sation with ease both ways ; but with the pair I have made 
tlie talking is loud, as I have several dodges on it." 

I repeated these experiments ; but the effect was so feeble as 
to be scarcely distinguishable, and, although interesting from 
a scientific point of view, it was of no practical value. 

Mr. James Blyth has independently repeated the experi- 
ment, and has shown that wood, paper, and india-rubber pro- 
duce similar effects. These effects are probably due to the 
fact that diamagnetic bodies have a similar though feebler 



Digitized by VjOOQIC 



292 Prof. P. E. Chase on Undulation. 

inflnence, in varying the direction of lines of magnetic force, 
to magnetic bodies. 

Again, I haye spoken distinctly and easily with telephones 
without any permanent magnet whateyer, the core of me coil 
being of soft iron ; but this effect was probably due to the 
impnriiy of the iron, residual magnetism remaining in it. Dr. 
Blake, of Boston, has spoken easily when the core was a piece 
of soft iron placed in the direction of the dip. 



XLI. On the Nebular Hypothesis, — ^VIT. Undulation, By 
Pliny Eaulb Chask, LL.D.y S.P.A.S.^ Professor of Phi- 
losophy in Haverford College, 

[Continued from tqI. It. p. 208.] 

THE combined inflnences of aethereal or auasi'^ihereal 
action and reaction, elasticity, density, ana ftmdamental 
velocity, in the arrangement of the Solar System, are shown by 
the symmetrical formula 

and by the equations, 

(!?!L)J^=x, . .' (2) 

4 
(|)W.=\ (3) 

S-l • • w 

Hk)'""- « 

5 5=^x1-061; (7) 

In these eouations fi ss mass of Sun ; /^ = mass of Jupiter ; 
fi^ = mass of Earth; X = average velocity of complete solar dis^ 
sociation := 214-86p-=-497-825 = velocity of light; Xi-2\/gp 
vs2 X velocity of incipient dissociation at Sun's sur&ce=mean 



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Prof. P. E. Chase on Undulation. 293 

radial Telociiy of complete solar dissociation 

^ 4x214'86*irp ^ 

number of seconds in 1 year * 

T s time of oscillation through major-axis equivalent to Sun's 
possible atmosphere, or to ^ of Earth's radius vector ; ti = 
time of Jupiter s revolution ; Ts = time of Earth's revolution; 
T3 as time of Earth's rotation ; p = Sun's equatorial radius ; 
pi =s Jupiter's projectile radius, or mean perihelion distance 
from Sun ;_n s special coefficient of Earth s dissociation velo- 
city (nirs/jr); ni= special coefficient of Jupiter's dissociation 
velocity (nx7r\//i^i); S « Earth's mean distance from Sun ; 
Si s= Jupiter^s secular perihelion distance from Sun ; S^ :s 
Uranus's mean distance from Sun ; 2* = relative radius of re- 
volution for 2t. ; 2* = relative time of revolution for ir^ ; 

^ not T -x > secular aphelion ,. , 

1-061 = Jupiter s radms vector. 

^ mean 

To illustrate the closeness of the accordances, if we substi- 
tute in (1) the actual values, viz. X=fl-f-2'317, Xi=p-r344'15, 
psl, pi= 1069*62, the equation reauces to 

//i±MiY^-»^1070-62; .-. ^^±^^ =1049-24. 
\ Ah / /*i 

Bessel's estimate is 1048*88, di£fering from the theoretical 
yalne only -J^ of one per cent. 

The signincance ot Earth's position, at the centre of the 
belt of greatest condensation, of the positions of Jupiter and 
Uranus, as inner planets of me two exterior two-planet belts, 
of the masses of Sun, Jupiter, and Earth, as the principal 
masses, in the system, in tne extra-asteroidaland in tneintra- 
asteroidal groups, and of the many important relations to the 
limiting veloci^ of luminous undulation, is thus clearly shown. 

In the sethereal waves which are generated bv the two con- 
trolling masses, fi and f^, we mav naturally look for harmonic 
interferences, not only in the solar spectrum, but also in ele- 
mentary molecular groupings and in cosmical masses. If we 
compare /i and /zi at Jupiter's present perihelion, we find that 
the product of Jupiter's radius vector oy its mass is 1*0153 
times the product of Sun's radius by its mass. Bepresenting 
1*0153 by a, and taking c=6(a— 1)=0*918, we may form the 

harmonic progression ——y ^ y » , Ac, thus obtaining 

the following nodal divisors and approximations, in millionths 
of a millimetre, to wave-lengths of Fraunhofer lines: — 



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394 Prof. P. E. Chase on Undulation. 

Denominatois. Nodal diyiBiona. Quotients. Obeerred. 

1 1-0000 761-20 A 761-20 

a + c(f) 1-1071 687-56 B 687-49 

[1-1530 660-19] C 656-67 

a + 2c 1-1989 634-92 

a-hScif) 1-2907 589-76 D 589-74 

a + 4c 1-3825 550-60 

[1-4437 527-26] E 527-38 

a+5c 1-4743 516-31 b 517-70 

a+6c(f) 1-5661 486-05 P 486-52 

a+7c 1-6579 459-13 

a + 8c 1-7497 43505 G 431-03 

[1-7650 431-27] 

a+dc 1-8415 413-37 

[1-9180 396-87] H 397-16 

a+10c(/) 1-9333 393-73 H 393-59 

The hannonic interferences which are indicated by the series 
marked (/) are the most interesting, both on account of the 
close accordance between the theoretical quotients and the 
corresponding observed values, and because the successive 
denominator-mcrements are figurate. Moreover the figurate 
series (1, 3, 6, 10) is the same as I pointed out in my equa- 
tion of products of triangular powers, which is applicable both 
to vector radii and to masses: — 

Of the six remaining lines, three (A, &, G) approximate so 
closely to the corresponding harmonic quotients, the greatest 
deviation being less than one per cent., that they may oe pro- 
perly regarded as illustrations of secondary interferences. The 
Dracketed divisors and quotients indicate tertiary harmonics, 
based on denominative differences of {/=a— ls=-0153, 1-1539 
«1 + 10(/, 1-4437=1 + 29(/, 1-7650=1 +50(/, 1-9180=1 
+ 60c'. The greatest difference between the theoretical and 
observed values is less than ^ of one per cent. ; all the other 
differences range between -^ and :Ar of one per cent. 

Among the subordinate spectral fines there are some which 
are closely represented by tne quotients of 761-20 by the de- 
nominators a + 2c, a + 4c, a + 7c, a + 9c. But, on account of 
the great number of faint lines, such accordances are less satis- 
factory than those which can be found in the lines that are 
more widely separated and more prominent. 

• Phil. Mag. for June (Supplement) 1876. 



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Prof. P. E. Cbase on Undulation. 295 

The following Table shows that, in planetary aggregation, 
the interference-waves have manifested their influence most 
strikingly at lominons intervals. The denominators are ex- 
ponential, indicating roots which are to be extracted, instead 
of divisions which are to be made. This is a natural conse- 
quence of condensation in and through an elastic medium. It 
wiU be noticed that the first six exponential denominators are 
arithmetical means between the nodal divisors in the foregoing 
Table, and that the others are formed by successive denomi- 
nator-increments of Jc. 

Observed. 

6453 Neptune. 

4122 Uranus. 

2050 Saturn. 

1118 Jupiter. 

728 Preia. 

473 Flora. 

327 Mars. 

215 Earth. 

155 Venus. 

110 Ven.-Mer. 

83 Mercury. 
64 „ s. p. 
53 „ c o. 

The observed values are the mean planetary vector radii, in 
units of Sun's radius. " Ven.-Mer." is the arithmetical mean 
between Venus's mean distance (155) and Mercuiy's secular 
perihelion (64). Mercury "c. o." is the centre of spherical 
oscillation (v^) of a nebula extending to Mercury's mean 
distance. 

The following comparisons show a few of the many har- 
monies which are found in the prominent lines of chemical 
elements. The wave-measurements in all the spectra, both 
solar and chemical, are taken from the papers of Prof. Wolcott 
Gibbs, in the * American Journal of ocience', second series, 
vols, xliii., xlvii. Kirchhoif 's lines are indicated by K ; Hug- 

S'ns's by H; Gibbs's groupings of corresponding lines in 
e groupings of both Kircnhotf and Huggins by KH — ^the 
left-hand columns containing Kirchhoff's estimates, and the 
right-hand columns those of Huggins: — 



Ezponentiid 


UnckiA 


denominators. 


X^UUbB* 


i-oooo 


6453 


1-0536 


4130 


1-1530 


2015 


1-2448 


1150 


1-3366 


708 


1-4284 


465 


1-5202 


821 


1-6350 


214 


1-7497 


150 


1-8644 


111 


1-9792 


84 


2-0939 


66 


2-2087 


53 



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296 



Prof. P. E. Chase on Undulation. 



Mercury, KH. 

WaTO-lengtiha. Quotients. Theoretical. 

568-47 568-55 1-0000 1-0000 1-0000 

546-33 546-13 1-0407 1-0411 1-0406 

542-80 542-80 1-0473 1-0484 1-0474 

Lead, EH. 

561-29 561-46 1-0000 1-0000 1-0000 

537-71 537-85 1-0439 1-0439 1-0440 

439-07 438-93 1-2784 1-2792 1-2784 

Butheniam and Iridiam, E. 

635-45 1-0000 1-0000 

545-44 1-1650 1-1646 

530-52 1-1973 1-1975 

Chromium, K. 

541-35 1-0000 1-0000 

621-20 1-0387 1-0387 

620-98 1-0391 1-0391 

520-83 1-0394 1-0394 

Arsenic, KH. 

617-54 617-67 1-0000 1-0000 1-0000 

611-69 611-67 1-0096 1-0098 1-0093 

578-95 578-73 1-0667 1-0673 1-0650 

533-55 533-41 11666 1-1580 1-1679 

Magnesium, E. 

518-73 1-0000 1-0000 

517-64 1-0021 1-0020 

517-17 1-0030 1-0030 

459-62 1-1286 1-1285 

448-57 1-1664 

448-39 1-1569 1-1570 

Zinc, KH. 

636-99 637-37 1-0000 1-0000 1-0000 

610-64 610-89 1-0432 1-0442 1-0390 

589-90 589-90 1-0798 1-0805 1-0781 

472-25 471-98 1-3488 1-3504 1-3613 



1 

l + 6a 

l + 7a 



1 

1+ 3a 

l + 19a 



1 

l + 6a 
l + 6a 



1 

1 + lIla 
1 + 112« 
l + 113a 



1 

1+ a 
1+ la 
l + 17a 



1 

1 + 
1 + 
1 + 



2a 
3a 
96 



1 + llJ 



1 

1 + a 
l + 2a 
l+9a 



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On the Kinetic Theory of Gravitatifln, -V/ ^^ 297 // 

Cadminm,KH. \) O^, "'^^S/, ^' 

WaTe-lengths. Quotients. TheoretiSal^ ^X/> ^' X 

647-22 647-08 1-0000 1-0000 1-0000 1.. ^ 0/> ', 

644-59 1-0041 1-0041 1-K&^28^\> 

531-27 531-01 1-2182 1-2186 1-2300 l + 2a "^ '- ( 

509-00 508-83 1-2715 1-2717 1-2727 l + 5ft 

480-56 480-27 1-3468 1-3473 1-3450 l + 3a 

468-10 1-3826 1-3818 l + 7i 

441-94 441-81 1-4645 1-4646 1-4600 l + 4a 

The qaotient of Kirchhoff's sixth wave-length by the seventh 
(468-10-f-441'94) is equal to the quotient of the fourth by the 
fifth (509 -=-480-56= 1-0592). 





Lanthanum, K. 






Wave-lengths. 


Quotients. 


Theorotical. 




538-56 


1-0000 


1-0000 


1 


538-43 


1-0003 


1-0003 


1 + ia 


538-00 


1-0011 


1-0011 


1 + a 


534-48 


1-0077 


1-0077 


1+ la 


520-80 . .. 


1-0341 


1-0340 


1+ 31a 


519-20 


10373 


1-0373 


1+ 34rt 


518-69 


1-0383 


1-0384 


1+ 35a 


481-59 


1-1183 


1-1183 


l + 108a 



XLII. The Bearing of the Kinetic Theory of Gravitation on 
the Phenomena of " Cohesion " and " Chemical Action,'* 
together with the important connected Inferences regarding 
the existence of Stores of Motion in Space. By S. Tolver 
Preston*. 

No. IVt. 
1. XT would be nataral to expect that any theory competent 
JL to explain the effects of gravity ought to be able to 
throw some light upon the subsidiary effects of molecules ex- 
hibited in " cohesion," " chemical action," Ac. Before pro- 
ceeding to consider this question, and in order to have a clear 
conception of the point we have to deal with, we will reca- 
pitulate in a few words the phvsical conditions involved in the 
case of gravity as already dealt with. It has been our object 
to point out that the molecules of a gas within the range of 
free path are moving in precisely the right way to produce 

* Communicated by the Author. 

t The three previous papNBrs treating of the sulnect of gmvitation are 
in the Philosopnical Magazine for September and November 1877, and 
February 1878. 



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298 Mr, S. T. Preston on the Khietie Theory of GravUation. 

gravity in two masses immersed in the gas within the range 
of free path. For since it has been proved from the kinetic 
theory that the particles of a gas adjust their motions so as to 
move uniformly or equally in all directions, and since the 
particles within the range of free path are moving in unbroken 
streams^ it follows that two masses immersed in the gas at a 
distance apart within this range will (owing to flie one 
sheltering the other^ be struck with more particles on their 
remote (unsheltered) sides than on their adjacent (sheltered) 
sides^ so that the two masses will be urged together. This, 
therefore, fulfils Le Sage's fundamental idea without the 
neoessitv for accepting any of his postulates. We need not 
accept tne scarcely realizable postulates of streams of particles 
coming from indefinite distances in space (at uniform angles), 
each stream moving continuously in one direction ; but we 
can substitute for this the natural conception of the normal 
motion of the particles of a gas within the range of free path, 
where, although each particle is continually changing the 
direction of its motion, yet the general character of the motion 
of the system as a whole remains unchanged ; or the system 
of particles automatically correct their motions so as to con- 
tinue to move uniformly or equally in all directions, as demon- 
strated in connexion with the kinetic theory of gases. This 
movement of the particles equally in all directions is the con- 
dition required to produce equal gravific eifect in all directions. 
Thus all we require to admit in order to produce all the efiects 
of gravity as necessary results, is the existence of a gas in 
space. Inis gas differs from an ordinary gas only as to scale, 
t. e, in the proximity, velocity, and extreme minuteness of its 
particles, wnereby a length of free path commensurate with 
the greatest observed range of gravity is insured, the extreme 
minuteness of the particles being at the same time adapted to 
that high velocity which the effects of gravity require, and 
which also necessarily renders the medium itself impalpable 
or concealed from the senses. The range of free path, though 
great in one sense, may be considered small and suitable for 
a gas that pervades the vast range of the visible universe. 

2. In applying these principles to cohesion, or the approach 
of molecules in chemical reactions, it is so far easy to see that 
when two molecules of matter come very close together, or if 
we suppose them actually to come into contact, then they will 
cut oft' the entire stream of particles of the gravific medium 
from between the parts in contact ; and therefore, as the gravific 
particles now only strike against the remote sides of Uke two 
molecules, the latter will be urged together with very great 



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Mr. S. T. Preston an the Kinetic Theory of Cfravitatian. 299 

force, thus explaining ^^ cohesion "*. But then a difiicnlty at 
once presents itself here. When two masses (or molecnles) 
are gradually approached towards each other^ instead of the 
tendency to approach gradually increasing up to a maximum 
(as we should expect from the theory)^ they begin to repel at 
a certain distance, and very considerable force is in general 
required to overcome this first repulsion, when the masses 
then unite into one. Thus two freshly cut pieces of lead may 
be made to unite with some pressure, also glass, or various 
metals, with more or less pressure. There is therefore a neutral 
paint which has to be passed, when the tendency to recede 
changes into a tendency to approach. The same thing is ex- 
hibited (conversely) when a substance is broken into two 
parts by tension. If pulled (nearly) up to the neutral point, 
the two parts recoil or return into their old positions. If pulled 
beyond the neutral point, the parts repel and will not return 
into their old positions, t. e, they separate permanently. The 
tiling, therefore, to be explained is the existence of this neutral 
point, or, in other words, the repulsion that exists at a certain 
distance from the surfaces. 

3. The explanation we have to offer here depends upon quite 
recent investigations. It must be observed first liiat facts 
prove the existence of a second medium in space besides the 
gravific medium, viz. the heat- or lighi>-convey mg medium (the 
aether). If we admit the existence of one medium in space 
constituted according to the kinetic theory (the gravific 
medium), it would & natural to conclude that the second 
medium (or sather) was constituted in an analogous manner. 
We shall give inaependent reasons afterwards that lead to 
infer this constitution, and endeavour to answer possible objec- 
tions ; but in the mean time it is only necessary to suppose it 
to be so constituted (in the absence of proof to the contrary) ; 
and if this supposition serves to explain in general principle a 
number of facts, this will be one argument for its truth. On 
account of the extreme shortness of the waves of light and 
beat, it would be reasonable to suppose that the length of free 

* The flpectroecope proves molecules to be complex >bodie8; on account 
of the nuniber of different periods of vibration they can take up ; and it 
was pointed out in the last paper that there are grounds for inferring them 
to possess interstices, or a more or less open structure. It is evident, 
therefore^ that the shapes of molecules, as to whether their parts fitted 
over each other or not (and thus afforded more or less shelter from the 
impinginff particles of the gravific medium), would have some influence 
on the behaviour of molecules as to the energy of their approach (reac- 
tions). This might account in some degree for the varied behaviour 
termed " chemical affinity,'' though possibly there are, besides this, other 
modifying physical conditions. 



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300 Mr. S. T, Preston on the Kinetic Theory of Gravitation^ 

f>atli of the aether particles was contained within compact 
imits^ or was^at any rate^ shorter than the length of the wave 
itself. It has been proved recently, in investigations by Mr. 
Johnstone Stoney in connexion with the radiometer*, that a 
medinm constituted according to the kinetic theory has a 
special power of propagating a pressure unequal in various 
directions, or that, when a layer of the medium (such as a layer 
of air) is intercepted between two surfaces whose distance 
apart is a small multiple of the length of free path of the 

f)articles of air, the layer can then transmit a pressure in the 
ine perpendicular to the surfaces which is in excess of the 
transverse pressure ; and thus a repulsion is produced, account- 
ing for the spheroidal state, the motion of the radiometer, &c. 
In fact it is evident (as pointed out) that, since in a medium 
constituted according to the kinetic theory the particles move 
in straight lines, the particles (when the distance of the opposed 
surfaces approximates to the range of free path) get reflected 
backwards and forwards repeatedly between the opposed sur- 
faces, the increments of energy received by the particles 
accumulating by successive reflections, so that the particles 
produce a bombardment tending to separate the two opposed 
surfaces t» The increments of velocity imparted by the neated 

* Philosophical Magazine, December 1877. 

t There is another point in connexion with the motion of the particles^ 
which no doubt, however, has been already noticed. Under normal con- 
ditions, a body vibrating opposite to another tends (as is known) to pro- 
duce rarefaction in the intervening medium ; but in the case of a film 
whose thickness is near the range of mean path of the particles, there 
would appear to be a special cause tending greatly to reauce this effect, 
and even perhaps to produce the contrary effect, viz. a condensation 
(which would greatly increase the repulsion). Thus, under the increments 
of velocity received, there is a tendency for the molecules of the gaseous 
film to be turned round so as to move more normal to the film. Suppose, 
for instance, an elastic sphere to be rebounding obliqtiely between two 
planes. Suppose increments of velocit;^ to be given to the sphere by vi- 
orating one of the planes. Then these increments of velocity given to the 
sphere will evidently make it rebound more normal to the surfaces. So 
in the case of the molecules of a gaseous film, reboimdinff backwards and 
forwards between two surfaces (such as the air film which supports a 
drop in the so-called ^' spheroidal *' state, the air film which supports a 
ffram of powder in some experiments of Professor Barrett, referred to by 
Mr. Johnstone Stoney), the molecules of the film will tend, by the incre- 
ments of velocity given them, to turn round so as to move in a direction 
more normal to the surfaces. This evidently makes the lateral pressure 
exerted by the film less, and consequently its lateral expansion (or rare- 
faction) less. If we imagine the extreme case where the molecules of the 
film are all turned round so as to move exactly normal to the surface of the 
film, then whatever the velocities of the molecules of the film (t . e, what- 
ever the lonffitudinal pressure, or repulsion, exerted by them), the film 
would exert no lateral pressure at all. There would consequently be a 
lateral inrush of air, increasing the density of the film, and therefore in- 



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Mr. S. T. Preston on the Kinetic Theory of Gravitation. 301 

surfaces are also mainly received in the line joining the 
surfaces (not so much transversely) ; so that this condaces to 
the pressure on the surfaces, or repulsion* 

4. This is precisely what we have to put forward, in its 
application to the oethery as an explanation of the repulsion in 
the cases referred to, such as for example the repulsion of two 
lenses or glass surfaces placed together in such proximity as 
to exhibit " Newton's rings," the repulsion of two molecules 
Ac ; for if the aether be constituted according to the kinetic 
theory, we shall inevitably have the same phenomena here, 
though on an infinitely more energetic scale ; for the particles 
of ffither come into direct contact with the vibrating molecules 
of matter, whose energy of vibration is known to be enormous 
at normal temperature ; and the layer of aether is very thin, 
and the motion of the aether particles very rapid*, so that the 
successive increments of velocity imparted by the vibrating 
molecules accumulate by successive reflections (backwards and 
forwards) between the opposed surfaces, producing a forcible 
repulsion. These results nave been theoretically demonstrated 
to follow on the basis of the kinetic theory, and have been 
established by experimental facts. It is a point of great im-* 
portance to observe that it is specially the kinetic theory that 
explains this othervrise most curious fact of an ewcess of pressure 
in a medium in one direction (producing a repulsion), with 
normal pressure existing in transverse directions, which other- 
wise it would be so difficult to explain, and which must be 
explained in order to account in a realizable manner for the 
phenomena observed. It is difficult to conceive how any 
other means of explaining this curious fact could be affi)rded 
than that supplied by the kinetic theory. Moreover it is 
generally admitted that heat has the property of producing 
repulsion. The ^' heat " of the molecules in the cases men- 
tioned is known to consist in their vibrations, by which they 
generate waves of heat in the aether. We have therefore to 
explain under what particular constitution of a medium tn- 
brations can (within certain limits) produce repulsion. The 
kinetic theory of the constitation of the medium solves com- 
pletely this peculiarly difficult problem. 

creasinff the repulsion (since those molecules which enter the iilm hecouie 
themseivee available for producing lepuleion). Possibly, from this cause, 
these films may be actually denser than normal density. At all events 
the ^bove cause makes their density greater than it otherwise would be, 
and the repulsion exerted by them greater. 

* It may be noted that, if the sBther be constituted according to the 

o 

kinetic theory, the normal velocity of its particles is — -— X velocity of a 

wave of light. See appendix to paper " On the Mode of Propagation of 
Sound " (Hiil. Mag. June 1877), added by Prof. Maxwell. 



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302 Mr. S. T. Preston on the Kinetic Theory of Gravitation. 

5. When the two surfaces (or two moleeules) are poshed 
up closer to each other, then the energy of the gravific medium 
directed against the remote sides of the molecules prevails 
more and more, since the matual sheltering-power of the 
molecules increases in an enormously rapid ratio as contact is 
neared, and so the unbalanced energy of the gravific medium 
directed with full force against the remote sides of the opposed 
molecules at length outweighs the action of the Intercepted 
sether particles, and the two molecules are propelled together 
(or unite). 

6. We may allude to a few examples serving to illustrate 
the application of the above principles. Supposing we take 
the common case of the ignition of a gas jet. Then when the 
gas is turned on, the molecules of gas and air mingle with 
each other and are known to be exchanging motion and re- 
bounding from each other, and yet they do not unite. Ac- 
cording to the above principles the molecules, as thev approach 
each omer in their encounters, are kept apart by the forcible 
vibrations (which the molecules are known to possess*) which, 
through the increments of velocity imparted to the particles 
of the intervening aether, produce a repulsion in the manner 
described, as soon as the molecules in their encounters have 
approached nearly within range of the mean path of the SBther 
particles. When aflame is applied to the jet, the rapidly 
moving gaseous molecules of whicn the flame consists naturally 
produce a disturbance, jostling some of the molecules of the 
mixture of gas and air against each other, so that the neutral 
point is passed, whereby the molecules are brought into such 
proximity that their mutual sheltering action causes the 
gravific medium to impinge with full energy upon their re- 
mote sides, thus urging the molecules together (producing 
combination). The molecules are thrown into forcible vibra- 
tion by the shock of approach, and become luminous through 
the energy of the waves thus generated by them in the sur- 
rounding aether. These vibrations of the compound molecules 
after combination naturally cause the forcible rebound of any 
other molecules that happen to be in their proximity, the 
disturbance thus set up sufiicing to efiect the successive 
(practically instantaneous) combination of the entire jet of 
gas. The same considerations of course apply to the practi- 
cally instantaneous combination (explosion) of a mixture (in 
definite proportions) of gas and air, by an initial disturbance 

* The molecules of matter in the gaseous state are known to possess, 
in addition to the translatory motion peculiar to that state, a vibratory 
motion, in virtue of which the molecules generate waves of regular periods 
iu the ffither (these periods having in many cases been measured oy the 
apectroscope). 



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Mr. S. T. Preston on t/ie Kinetic Theory of Gravitation^ 303 

{^oduoed by a flame. In the case of solid bodies^ where the 
molecules are fixed or under control, a forcible pressure or 
concussion may serve to bring the molecules over the neutral 
point (sLud thus effect combination), as illustrated by the effect 
of the dIow struck in ^^ percussion " powders. It would not 
appear that matter in the gaseous state could ever be exploded 
by pressure (so long as the gaseous state was retained) ; for 
the molecules of gases cannot be pressed against each other by 
any amount of pressure, since, the molecules being in free trans- 
latory motion among themselves, the only effect of pressure 
would evidently be to put a greater number of molecules into 
unit of volume, without thereoy causing the molecules in their 
encounters to approach nearer to each other than before. The 
degree of approach of the molecules (in their encounters) 
depends evidently on their momentum or velocity ; and this 
remains the same whatever the pressure. 

7* Heat could not apparently oe said to augment the energy 
of chemical combination, since, in general, heat is known to 
possess the exactlv opposite effect, or to disintegrate matter. 
U^e part played by heat in effecting chemical combination 
would seem to consist simplv in producing a molecular die-- 
turbancej whereby unavoidably some molecules are urged to- 
wards each other so as to pass the outer neutral point, which 
is the necessary preliminary to combination. No doubt, when 
heated elements combine, the original heat adds itself to the 
work thus to be derived, as the heat cannot be destroyed, 
though it cannot increase the work of combination. Heat 
may (as is known) entirely prevent chemical combination, and 
even dissociate combined elements. The action of heat in 
preventing chemical combination and producing dissociation 
would on the above principles consist m the fact that, when 
the vibratory motion of the molecules becomes excessive, this 
vibratory motion generates sudi a pressure in the intervening 
layer of aether on the approach of the molecules as to pr^ent 
them from passing the neutral point : or, indeed, no neutral 
point may exist, provided the pressure or repulsion thus 
generated be such as to outweigh the action of the gravific 
medium, as appears actually to take place in the dissociation 
of matter by excessive heat. Thus it would appear probable 
from this, tnat when combination ensues in the case of a mix* 
ture of gases previously considerably heated (but not so much 
so as to produce dissociation), the molecules on combination 
do not at once settle down into that full proximity (which 
belongs to a lower temperature), but they do so gradually as 
the temperature falls. Thus the work of combination is pro- 
longed over the falling temperature, and the cooling thereby 



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304 Mr. S, T. Preston on the Kinetic TJieory of Gravitation. 

somewhat retaixled. Precisely the same thing is iUnstrated in 
the aggregation of groups of molecules (to form masses), as in 
the aggregation of single molecules to form oompoond 
molecules. Thus when a bar of iron is welded by heat, tiie 
molecules (though aggregated or combined) do not settle down 
into their final positions of proximity until the bar cools, the 
bar being observed to contract on cooling. In this instance 
also the cooling of the bar is somewhat retarded by the approach 
of the molecufes in the act of cooling. 

8. In the case of the ignition of a solid body, the same con* 
siderations no doubt apply as in the case of a gas. Thus, for 
example, the molecules of oxygen are impinging against the 
surface of a piece of coal, but do not produce ignition. To 
effect this a certain number of the molecules must be impelled 
with sufficient energy against the coal so as to carry them over 
the neutral point (i. e. beyond the initial repulsion). The 
application of a flame, which consists of matter in a state of 
violent agitation, suffices to effect this, and, no doubt by 
loosening some of the molecules of carbon (of the coal) and 
giving them translatory motion and mixing them with the air, 
mcilitates the process. 

9. As a further illustration of the exact similarity of behaviour 
of single molecules and groups of molecules (masses) as regards 
the existence of the above-mentioned neutral point, we may 
take the case of the substance iodine. This substance gives 
off a visible vapour at normal temperatures. The single 
molecules of iodine composing the vapour rebound from each 
other vrithout uniting ; and this can only be due to the exist- 
ence of the above-mentioned neutral point, outside which there 
is a repulsion. If the colliding molecules were to approach 
within the neutral point, they would unite and form solid 
iodine. No doubt some of the molecules of the vapour (as 
their velocities are known to be very diverse) do pass beyond 
the neutral point; and thus molecules of vapour striking against 
the fragments of solid iodine in the bottle, will sometimes 
unite with the solid iodine and form part of it, while, on the 
other hand, other molecules of the solid which happen to pos- 
sess excessive vibrating energy are thrown off, this being the 
known way in which tne balance in evaporation is maintained. 
The masses of iodine have the same neutral point as the 
single molecules, since two masses of the substance when 
pressed together will not readily unite ; u e. the neutral point, 
where the outer repulsion terminates, must be passed first*. 

♦ The above effects were described in a little book ' Physics of the 
Ether' (E. & F. N. Spon), puhlished hy me in 1875 ; hut the catue of the 
reduction of the pressure or the medium, which determines the approach 



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Mr. S. T. Preston on the Kinetic Theory of Gravitation^ 305 

10. Just as increase of vibrating energj (temperatare) 
tends, by the increase of pressure thus produoed in the inter- 
vening film of the medium, to dissociate molecules, so reduc- 
tion of vibrating energy (attendant on reduction of tempera- 
ture) tends to facilitate the approach of molecules, on account 
of tJie reduction of the pressure or repulsive action of the 
intervening film. Thus the molecules of a vapour when their 
vibrating energy is reduced (by a fall of temperature) may by 
the simple momentum of their own encounters, carry them- 
selves over the neutral point, and thus effect the condensation 
of the vapour. Numerous other cases might be cited illustra- 
tive of the application of the above principles, as, indeed, the 
molecular effects are very similar in their fundamental aspects. 
The molecular phenomena, however diverse, may be all corre- 
lated in one fundamental respect, viz. as consisting in phe- 
nomena of approach and recession. The fundamental condi- 
tions to be explained, therefore, are the conditions capable of 
producing the approach and recession of molecules. W hatever 
may be said of the above deductions, it is at least so far certain 
that the conditions investigated, and based upon experimental 
fiEicts, are competent to produce these fundamental movements 
of approach and recession in the case of molecules, and to do 
so in the simplest manner, the constitution of media according 
to the kinetic theory being admittedly the simplest conceivable. 
To look therefore to other conditions thaii the simplest would 
be to imply that the same results are brought about by a 
superfluity of mechanism. This superfluity is known not to 
be the characteristic of nature ; and all the teaching of 
mechanism points to the fact that superfluity or unnecessary 
complication entirely prevents the attainment of precision and 
certainty in the mechanical effects. The great precision and 
unfailing certainty of the molecular effects would therefore 
render it necessary to infer that the regulating mechanism was 
simple, or that there was no unnecessary superfluity. 

11. The fundamental conclusion above drawn regarding 
the mechanism concerned in the approach of molecules is 
grounded upon the only explanation of the mechanism of 
gravity that has withstood criticism and received support bv 
competent judges, viz. the kinetic theory of gravity, of which 
Le Sage's ingenious idea forms the fundamental basis, and is 
at once the simplest explanation of gravity conceivable. The 

of molecules, was there wrongly stated, the error haTing arisen from a 
seeming analogy between the approach of bodies to masses (tuning-forks 
&c.) vibrating m air — in the absence of the knowledgje recently acquired 
of the repulsion of gaseous layers. Much of the main principles of the 
book, however, remain as they were — ^to be supplemented by the investi- 
gatioDs contained in the present papers. 

Fhil. Mag. S. 5. Vol. 5. No. 31, April 1878. X 

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306 Mr. S. T. Preston an the Kinetic Theory of Gravitation. 

application of this theory to molecules in dose contact (" co- 
hesion " &C.), 19- necessary and inevitable, and it serves to cor* 
relate the molecular effects generally under one cause. The 
explanation of the fundamental condition capable of producing 
the recession of molecules, as above given, rests upon experi- 
mental facts recently established, and upon a basis for the 
constitution of the aether which is the simplest conceivable. 

12. We now propose to show some independent reasons in 
support of this constitution for the sether, in addition to the 
argument afforded by the numerous molecular effects which 
this constitution, in principle, serves to exnlain. First, if 
the subject be reflected on, it will be apparent tnat, in principle, 
a movement of the component particles of the medium in 
straight lines is the only possible constitution for the ultimate 
medium in space. For a particle of matter cannot move in a 
curved line unless it have a medium about it to control its 
motion. Thus a planet can move in a curve because it has a 
medium about it (the gravific medium) to cause it to move in 
a curve. It is a known principle that a particle of matter canr- 
not of itself change the direction of its motion. The particles 
of the ultimate medium in space must therefore move in straight 
lines. This deduction is surely of great importance in the 
inquiry as to the constitution of the physical media in space. 
Also in addition to this, the obsei-ved facts of gravity prove 
that the particles of the gravific medium move in straight 
lines, since no other motion than this can harmonize with the 
observed effects of gravitv. It would therefore surely be a 
strange thing if the particles of the aether, as a second medium 
immersed in the gravific medium, did not move in straight 
lines. To suppose this would be very like supposing t£at 
when the particles of a second gas are immersed among those 
of another, the particles of the first gas acted upon those of 
the second to make them move otherwise than in straight 
lines, which is known to be impossible. Moreover the ract 
of the kinetic theory representing the simplest conceivable 
constitution for a medium would by itself be a strong argu- 
ment for this constitution in the case of the aether. iSie very 
fact of the great nrecision and delicacy of the operations per- 
formed by me aether as the mechanism for the transmission of 
the varied phenomena of colour &c. would point to a simple 
constitution ; just as the complex effects of sound with all its 
intricate and varied gradations of tone are known to be trans- 
mitted by a medium (the air) of the simplest conceivable con- 
stitution, viz. that represented by the beautiful kinetic theory 
of gases*. The more intricate the functions of a mechanism, 

• There would suxely be nothing to admire in complication in itself. 
The whole aim of mechanical design is directed towards the attainment 
of nmpUcity, which being uniquCf entails intellectual labour to find it. 

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Mr. S. T. Preston on the Kinetic Theory of Gravitatum. 307 

the more is simplicity indispensable^ and superflui^' incom« 
patible with precision and certainty in the results. To assume 
a constitntion for the SBther that could not be realized or 
clearly explained would surely be futile^ since the explanation 
or clear conception forms the logical support of any theory^ 
without which the theory resembles a mere dogmatic state- 
ment incapable of being sustained by reason. 

13. There is one other point which we would notice in con- 
nexion with this subject. The idea would appear to be to a 
certain extent prevalent that the ssther must have a constitu- 
tion essentially different from the air^ because the vibrations 
producing light are transverse^ while those producing sound . 
are longitudmal. It seems to be sometimes inferred from 
this that the vibrations of the SBther are onli/ transverse, and 
those of the air on/y longitudinal. There would be no warrant 
for this conclusion ; and we think that it has done barm and 
greatly hindered any rational idea from being formed of the 
natare of the aether. According to the kinetic theory, which 
is known to represent the constitution of the air, the vibrations 
of the particles of air disturbed by a vibrating body and pro- 
pagated in the form of waves, are not onlt/ longitudinal ; for 
since according to the kinetic theory the particles of air in 
their normal state are moving equally in all directions, it 
follows that these particles are accelerated and retarded both 
in transverse and in longitudinal directions at the passage of 
waves. It is true that the transverse component of the motion 
probably may not affect the ear, on account of its special 
structure. It would be wrong, however, to infer from this 
that the transverse component of the motion did not exist. 
So in the case of the aBther, it would be unwarranted to infer 
that the longitudinal component of the motion did not exist, 
because this component was incapable of affecting the eye. 
The eye and the ear may be very aifferently constituted ; and 
a motion that affects the one might not affect the other. Sir 
John Herschel says regarding this point in his essay '^ On 
Light" ('Popular Lectures on Scientific Subjects,' page 
358) : — '• According to any conception we can form of an 
elastic medium, its particles must be conceived free to move 
(within certain limits greater or less according to the coercive 
forces which restrain them) in every direction." He then 
goes on to explain how the efficacy of the transverse component 
of the movement in the case of light, and the longitudinal 
component of the movement in the case of sound, may be ac- 
counted for by the diverse structure of the eye and ear. Any 
inference which is not valid, invariably does some harm ; and 
this idea of a forward movement being propagated in a'medium 
by Ofily transverse vibrations, being almost mconceivable, has 

X2 

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808 Mr. S. T. Preston an the Kinetk Theory of Gravitatian. 

natnrallj led to some incongraous ideas regarding the sirao- 
ture of the SBther, in the effort to explain it. Thns some have 
supposed the aether to resemble a solid, which is in direct 
opposition to the teaching of the senses ; for we move about so 
freely in this " solid " as to be unconscious of its existence. 
Another supposition has been that "lines of tension," behaving 
somewhat in analogy to stretched chords, exist in the aether. 
Such a mechanism would be, to say the least, somewhat de- 
ranged by the passage of a planet through the aether. Indeed 
it is sufficiently eyident that these are the hopeless attempts 
made to surmount an impossible condition, or a difficulty for 
whose existence there is really no warrant. If the aether be 
not a solid, or a liquid (for liquids oppose enormous resist- 
ances to the passage of bodies through them at high speeds), 
then what other resource have we than to conclude that it is 
a gas? 

14. A gaseous constitution of the aether according to the 
kinetic theory would perfectly satisfy the two fundamental 
conditions of a medium highly elastic in all directions, and 
opposing no appreciable resistance to the free movement of 
bodies (the planets &c.) through its substance. For it is a 
known fact that the resistance opposed by a medium consti- 
tuted according to the kinetic theory to the passage of bodies 
through it diminishes as the normal velocity of the particles 
of the medium increases. The high normal velociiy of the 
particles of the aether, proved by the velocity of li^ht, uierefore 
necessarily renders the resistance inappreciable, ana the medium 
itself impalpable and undetected by the senses. 

15. A difficulty has been raised in the way of the aether 
being constituted as a gas on the following grounds, which, 
being only anxious for truth, we are bound to consider *. It 
has been argued that if the aether be constituted as a gas, the 
specific heat of unit of volume of the aether would be the same 
as that of' any ordinary gas at the same pressure, and that 
therefore it would appear that the presence of the aether could 
not fail to be detected in the experiments on the specific heat 
of ordinary gases. We have to offer the following as a means 
of meeting this difficulty. It will be admitted that the de- 
tection of the aether in the experiments on specific heat will 
depend, not on the specific capacity for heat possessed by the 
aetner, but on the rate at which the heat passes from the gas 
experimented on to the aether. The molecules of the gas are 
moving through the aether with their normal translatory 
motion, this motion of the molecules representing the "heat ' 
of the gas. It will be evident that the rate at which the 

* See paper " On tlie Dynamical Evidence of the Molecular Constitu- 
tion of Bodies," by Prof. Maxwell (* Nature/ March 11, 1875). 

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Mr. S. T. Preston on the Kinetic Theory of Gravitation* 309 

motion (" heat ") of the molecules of the gas passes to the 
»ther will depend on the resistance the aether offers to the 
passage of these molecules through it. But we have shown 
that mie resistance may (on account of the high normal velo- 
city of the aether particles) be inappreciable. Hence the rate 
of passage of the neat from the gas to the sether will be inap* 

fireciable. This, we submit, removes the diflSculiv in question. 
t is clear that, if the aether opposes no appreciable resistance 
to the passage of a planet through it (moving at several miles 
per second), it cannot be affected bv the passage of a molecule 
of a gas through it, which in its relatively slow rate of trans- 
latory motion may be considered at rest compared vriih the 
aether particles. The high normal velocity of the aether 
particles is only appropriate to their minute mass. 

16. It must be apparent to any reflecting observer, that in 
physical science we nave a vast array of facts accumulated 
through years of experiment, but a great paucity of causes ; or 
the number of facts Jknown is quite out of all proportion to the 
number of causes known, these latter being replaced by more 
or less vague and unsubstantial theories. As, therefore, we 
have no paucity of facts as a basis to reason upon, it surely 
cannot be too soon to make an effort to correct this anomalous 
state of things, and to replace the above unsubstantial theories 
by rational conceptions of the processes of nature, Clearness 
of conception is the test of truth, and constitutes its real dignity ; 
and theories, however elaborated, if vague, have no real dignity*. 
Since there is nothing occult about the physical media in space, 
in so far as they differ in no way from ordinary matter ex- 
cepting in the mere scale or dimensions of their parts, and 
since it is obviously just as easy to reason of matter of one 
dimension as of another, any hesitation in entering upon this 
course of study would be wholly uncalled for ; indeedyjsur^iy 
there is reason for a rational interest in realizing the admirable 
adaptation of these media in a mechanical pomt of view for 
their special Amotions ; and the question as to the utilization 
of the stores of motion enclosed by them to the best advantage 
may present a problem of the highest practical interest and 
importance f. It should be observed that these stores of 

* Vagjienees, paradox, and mystery surely belong rather to those intel- 
lects wmch are incapable of rising to clear and definite conceptions. 

t As an instance of the chan^ of views on the most practical subjects 
that the acceptance of these pnncinles entails, we may cite the case of 
the employment of coal, which by tne recognition of the existence of the 
stores of motion in space, becomes a mechanigm or machine for deriving 
motion. The expenditure of coal, therefore, represents the expenditure 
of mechanism or machinery. Hence in deriving motion through coal we 
expend a auantitv of machinery proportion&i to the power derived. 
Without asking the question whetner it is necessary in every case, in 
deriving motion from a source, to expend machincr}' proportional to the 

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310 kr. S. T. Preston on the Kinetic Theory of Gravitatian. 

motion simply consist in small particles of matter in a state of 
rapid motion ; or there is nothing occolt about the subject at 
all, as indeed obvionslj principles of reasoning are independemt 
of size. The minute size (and consequent invisibility) of the 
particles is necessary to the efficiency of the media as powerful 
motive agents, since minuteness of size is necessary to render 
a high velocity possible for the particles, without producing 
disturbing effects among the matter immersed in these media. 
There is one very noteworthy point that cannot be too dis- 
tinctiy kept in view in connexion with this subject. It is the 
fact that the high intensity of the stores of motion possessed 
by these media, and which renders them so important, serves 
to conceal their existence from the senses. Tnus the higher 
the intensity of the store of motion enclosed by these media, 
and consequently the greater their capacity for practical 
utility, the more likely (if the mere evidence of the senses 
were relied on) is their existence to be forgotten. For it may- 
be proved beforehand, by the kinetic theory of gases, that the 
greater the velocity of the component particles of a medium, 
and consequently the greater tfie value of the store of enenjy 
enclosed (which may even reach an explosive intensity), the 
more does the presence of the medium elude detection, b^nse 
the resistance opposed by the medium to the passage of bodies 
through it diminishes as the velocity of the particles increases. 
The less indication the mere senses (unaidea by reason) afford 
of the existence of such media, the higher, therefore, should 
we be warranted in inferring their importance to be. Even 
independently of all question of the existence of these media^ 
it may be proved beforehand that, if media did exist and en* 
close stores of motion to an enormous intensity, they tpovld be 
concealed. This is, no doubt, a remarkable fact, and contrary 
to preconceived ideas, as it would doubtiess appear on the first 
thought that the higher the intensity of a store of energy ex- 
isting in space, the more likely would it be to make itself 
apparent to the senses, whereas precisely the contrary is found 
to DC the fact. This forms a notable instance of one of those 
cases where analysis completely reverses preconceived ideas. 
It is possibly the absence of appreciation of this &ct that may 
in some way account for the failure of the most striking proofs 
of nature to carry their practical teaching, as for example,, 
the sudden setting free of concealed motion in the explosion 
of a mass of gunpowder. Here to the mere bodily senses, we 
have apparentiy an actual creation of motion. Something 

power derived (t. e, that the work done should be the equivalent of the 
machinery expended), it is at least so far certain that no remedy for this 
could be discovered unless the physical conditions of the case were re- 
cognized. 

Digitized by VjOOQIC 



Notices respecting New Boohs, * 311 

more^ bowerer, than the evidence of the mere bodily senses 
may be required, to appreciate the troths of nature, as it is a 
notorions ract that the most important traths generally lie 
below the surface. It should be noted that these media would 
not be efficient as working agents unless thoy were concealed ; 
for concealment (as observed) is the necessary condition to the 
enclosure of a store of motion to a high intensity. Possibly 
the absence of realization of this fact, and perhaps that pre- 
judice which besets every new path, may in some degree 
account for what must otherwise appear an extraordinary 
indifference and absence of inquiry in a subject of great me- 
chanical interest and involving possibly issues of the highest 
importance and practical utility. When this, like every other 
illogical prejudice to change, comes to be broken down by the 
light of reason and reflection, there may be just ground for 
surprise at the previous delay^ and at the shallow and unsub- 
stantial character of the theories which so long supplanted 
rational conceptions of the processes of nature. 
London, March 13, 187?. 

XLIII. Notices respecting Neio Books. 
J)e^ ParaUmnerres a Pointes a Conducteurs et a RaccordemenU Ter- 
restres Multiples. Description detaillee des Paratonnerres Stablis sur 
r Hotel de VUle de Brv^elles en 1865. Expose des motifs des dis- 
positions adopties par Melsens, Memhre de VAcadSmie Royale des 
Sciences de Belgique. Bruxelles : Hayez. 1877. 
T^HE work, of which the title is given above, possesses an interest 
-*- not only to the electrician and man of science, but to the 
architect and antiquary; and Professor Melsens, already so favour- 
ably known to the world of science, has done further good service 
in applying sound scientific principles to the preservation of those 
grand monuments of roedissval architecture of which his country is 
so justly proud. The origin of the work which we now notice was 
in the circumstance that, in a thunder-storm in 1863, one comer 
tower of the Hotel de Ville at Bruxelles was struck by lightning, 
and that portion of the building seriously injured, whilst the very 
much higher central tower and spire were not touched. The muni- 
cipal authorities of Bruxelles at once proceeded to consider the steps 
to be taken to preserve the building from any future like injury, 
and requested the assistance of the Academy of Sciences, which 
appointed a committee. Opinions were very much divided, and no 
practical conclusion was arrived at; so the Municipal Council 
very sensibly passed over the Committee and placed the whole 
matter in the hands of Professor Melsens, who had formed definite 
ideas on the subject, and was prepared to take the responsibility of 
carrying them out. The great difference of opinion among scientific 
men was as to the comparative advantages of concentrating the 
means of defence in one or a very few lightning-conductors ex- 
tended to a great height, overtopping the most elevated portions of 

Digitized by VjOOQIC 



312 NoticeB rtspeding New Booh. 

the building, but leftving the lower porfcionB snd general mass d 
the building unprotected, or (2) of supplying all, even the lower 
portions of the edifice, with conductors of lesser height and dimen- 
sions, but all connected among themseWes, and all leading finally 
to some great conducting mass of earth or water into which tlw 
electric discharge should finally find issue. M. Melsens was led to 
conclude decidedly in favour of the latter plan, and to adopt in 
electricity, as is often done in public matters, the maxim divide H 
impera. He was struck with the fact that, although dating from 
1400, the Hotel de ViUe had never been struck by li^tning 
until the present century, and has since been struck several times, 
although seriously damaged only on the last occasion, in 1863. He 
attributes this remarkable immunity of four centuries to the ainomit 
of gilding and metallic decoration &c., which almost coTered over 
the surface of the building in the later middle ages and down to 
the end of the last century — the projecting pinnacles and statues 
especially having been then blazing with gold and brass, thus fur- 
nishing an enormously extended, if superficial, issue for the electric 
discharge. On the other hand, in the case of the List thunder-storm 
he finds the greatest injury to have occurred where parts of the 
towers and pinnacles were supported by iron bars which were un- 
connected with each other or with the ground. Where perfect 
connexion existed, even, as in the case of the great clock, by a fev 
thin wires, the electric discharge passed harmlessly along ; and the 
fortunate escape of the great central spire from destruction is thus 
to be accounted for. 

Acting on those principles, M. Melsens devised an arrangement 
for investing the Hotel de Ville with a connected series of conduc- 
tors moderate in mass and in height, terminating on each projecting 
eminence of the building in pencils of wire, but not prominently 
interfering with the architectural characteristics. In this way the 
edifice is surrounded by a complete cage of iron wire, so that a~ flash 
of lightning striking on any point must be immediately subdivided 
into a multitude of parts and so diluted as to be render^ innocuous. 
This iron cage is in its turn connected with what M. Melsens terms 
the subterraneous paratonnerres, consisting of the whole system ol 
pipes employed in the gas- and water-distribution of the city ; and, 
Irom the details of the mechanical arrangements ^ven, this con- 
nexion is of the most perfect kind. On this pomt M. Melsens 
lays considerable stress, as he believes that very many lightning- 
conductors of the ordinary kind are rendered useless practically l^ 
the imperfect connexion with a sufiicient mass of earth and wat^ 
conductor. We must refer to the work itself for all the mechanical 
details by which M. Melsens's ideas have been practically carried 
out, and which are copiously illustrated by engntvings. We shall 
not either enter into the discussion as to the merits of the questions 
still at issue among practical electricians of great eminence and ex- 
perience. M. Melsens gives in his book a full and fairly stated 
rUume of the arguments and evidence against as well as in favour 
of his own views ; and that his views, even when deviating from 
the traditional decisions of scientific authorities (as, for example, ol 

Digitized by VjOOQIC 



Geological Society, 313 

the Paris Academj of Sciences), haye been approyed and acted 
upon bj competent judges, is shown bj the fact that the charge of 
preserring from further electric injury the grandest architectural 
monument of Belgium has been intrusted to his care. 

We recommend Professor Melsens's work to the careful perusal 
of all who are interested in the preservation from injury by light- 
ning of ships and buildings, as well for its useful mechanical sug- 
gestions as for its interesting and accurate scientific details. 

XLIV. Proceedings of Learned Societies. 

GEOLOGICAL SOCIETY. 

[Continued from p. 237.] 

January 23, 1878.— Prof. P. Martin Duncan, M.B., FJt.8., 

President, in the Chair. 

THE following communication was read : — 
1. <' On the Secondary Eocks of Scotland.— Part III. The Strata 
of the Western Coast and Islands/* By John W. Judd, Esq., P.R.S., 
F.G.S., Professor of Geology in the Eoyal School of Mines. 

The existence of scattered patches of fossiliferous strata lying be-> 
tween the old gneissic rocks and the masses of Tertiary lava in the 
Hebrides, has been known to geologists for more than a century. 
By Br. Macculloch, who did so much for the elucidation of the in- 
teresting district in which they occur, these strata were referred to 
the Idas ; but Sir lloderick Murchison showed that several members 
of the Oolitic series were also represented among them. Later 
researches have added much to our knowledge of the more accessible 
of these isolated patches of Jurassic rocks in the Western Highlands. 

During the seven years in which he has been engaged in the study 
of these interesting deposits, the author of the present memoir has 
been able to prove that not only is the Jurassic system very 
completely represented in the Western Highlands, but associated 
with it are other deposits representing the Carboniferous, Poikilitic 
(Permian and Trias), and Cretaceous deposits, the existence of which 
in this area had not hitherto been suspected ; and by piecing to- 
gether all the fragments of evidence, he is enabled to show that 
they belong to a great series of formations, of which the total 
maximum ^ckness could have been little, if any thing, short of a mile. 

The relations of the scattered patches of Mesozoic strata to 'the 
older and newer formations respectively, are of the most interesting 
and often startling character. Sometimes the secondary rocks are 
found to have been let down by faults, which have placed them 
thousands of feet below their original situations, in the midst of 
more ancient masses of much harder character. More usually they 
are found to be buried under many hundreds, or even thousands of 
feet of Tertiary lavas, or are seen to have been caught up and en- 
closed between great intrusive rock -masses belonging to the same 
period as the superincumbent volcanic rocks. Occasionally the only 
evidence which can be obtained concerning them is derived from 
fragments originally torn from the sides of Tertiary volcanic vents, 
and now found buried in the mined cinder cones which mark the 



Digitized by VjOOQIC 



314 Oeoloffieal Society: — 

sites of those Te&ts. In some cases the mineral charaoters of the 
strata have been greatly altered, while their fossils hare been oeoa- 
sioDally wholly obliterated by the action of these same igneons forces 
daring Tertiary times. 

In every case the survival to the present day of the patches of 
Secondary rocks can be shown to be dne to a combination of most 
remarkable accidents ; and a stndy of the distribution of the frag- 
ments shows that the formations to which they belong originally 
covered an area having a length of 120 miles from N. to S., and a 
breadth of 50 miles from E. to W. But it is impossible to doubt 
the former continuity of these secondary deposits of the Hebrides 
with those of Sutherland to the north-east, with those of Antrim to 
the south, and with those of England to the south-east. From the 
present positions of the isolated fragments of the Mesozoic rocks, 
and after a careful study of the causes to which they have owed 
their escape from total removal by denudation, the author con- 
cludes that the greater portion of the British islands must have 
once been covered with thousands of feet of secoDdary deposits. 
Hence it appears that an enormous amount of denudation has gone 
on in the Highlands during Tertiary times, and that the present 
features of the area must have been, speaking geologically, of com- 
paratively recent production — ^moet of them, indeed, appearing to be 
referable to the Pliocene Epoch. 

The alternation of estuarine with marine conditions, which had, 
on a former occasion, been proved to constitute so marked a feature 
in the Jurassic deposits of the Eastern Highlands is now shown to 
be almost equally striking in the Western area ; and it is moreover 
pointed out that the same evidence of the proximity of an old 
shore-line is exhibited by the series of Cretaceous strata in the West 

The succession and relations to one another of the series of 
deposits, now described as occurring in the Western Highlands, is 
given in the following Table : — 

Miocene Volcanic and Intervolcanic Bocks. 

Ulf CONFORMITY. ' 



I 



Max. thickni 
feet 

1. Estuarine clays and sands with coal 20+ 

2. White Chalk with flints (Zone of Belenmitella ffmcro- 

nata) 10+ 

3. Estuarine Sandstones with coal 100 

4. Upper Greensand beds 60 

Uncowpormitt. 

5. Oxford clay ? 

6. Great Estuarine Series 1000 

7. Lower Oolite 400 

8. Upper Lias 100 

9. Middle Lias 500 

10. Lower Lias 400 

11. Infraliaa 200 

12. Poikilitic 1000+ 

Uhconformity ? 

Carboniferous strata (Coal-meaaures). 



UWCOWFORMITY. 

Old Gneisi Series and Torridan Sandstones, 



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On Hie Strata of the Western Coast and Islands^, 815 

Although no traces of the Upper Oolite or the Neooomian forma- 
tions have as yet been detected in the Western Highlands, yet it 
is argued that when we consider how enormous has been the amount 
of denudation, and how singular the accidents to which all the ez-^ 
iflting relics of the Secondary period have owed their escape from 
total destruction, we cannot but regard it as a most rash and 
unwarrantable inference to conclude that no deposits belonging to 
those periods were ever accumulated within the district under consi- 
deration. 

The Carboniferous strata of the Western Highlands have been 
detected at but a single locality, and even there, being exposed in 
a series of shore-reefs that are only occasionally well displayed, 
can only be studied under favourable conditions of tide and wind. 
They consist of sandstones and shales with thin coaly seams ; and 
their age is placed beyond question by the discovery in them of 
many well-known plants of the coal-measures, including species of 
Lepidodendrony Calamitety Sigillaria^ and Stigmaria. 

The Poikilitic strata consist of conglomerates and breccias at the 
base, graduating upwards into red marls and variegated sandstone, 
which contain concretionary limestones and occasional bands of 
gypsum. These strata have not as yet, like their equivalents in 
^e Eastern Highlands (the Eeptiliferous Sandstone of Elgin and 
the Stotfield rock), yielded any vertebrate remains. They were 
evidently deposited under similar conditions with the beds of the 
same age in England, and are not improbably of lacustrine origin. 

The Jurassic series presents many features of very great interest. 
The Infralias is better developed than is perhaps the case in any 
part of the British Islands ; and in the district of Applecross a series 
of estuarine beds containing thin coal-seams is found to be inter* 
calated with the marine strata. 

The Lower lias, in its southern exposures, presents the most 
striking agreement with the equivalent strata in England, but 
when traced northwards exhibits evidence of having been deposited 
under more littoral conditions : the lower division (Lias a, Quen- 
stedt) is represented by a great thickness of strata ; while the upper 
(Lias /3) is absent or rudimentary. The Middle Lias is grandly de- 
veloped, and consists of a lower argillaceous member and an upper 
arenaceous one, the united thickness of which is not less than 
500 feet. The Upper Lias singularly resembles, in the succession 
of its beds and its palsBontological characters, the same formation 
in England. The Inferior Oolite is formed by series of strata 
varying greatly in character within short distances, and betraying 
sufficient signs of having been accumulated under shallow-water 
conditions. Above the Inferior Oolite we find a grand series of 
estuarine strata, partly arenaceous and partly calcareo- argillaceous ; 
and this is in turn covered conformably by an unknown thickness 
of blue days with marine fossils of Middle Oxfordian age. At the 
very lowest estimate, the Jurassic series of the Western Highlands 
coidd not have had a thickness of less than 3000 feet ! 

The Cretaceous strata of the Western Highlands, though of no 
great thickness, are of surpassing interest. They consist of two 



Digitized by VjOOQIC 



316 Geological Society, 

marine series altematiiig with two others of estnarine origin. At 
the base we find marine deposits of Upper Greeasand age, strikingly 
similar to those of Antrim, but in places passing into oonglomerateB 
along old shore-lines. Above the Upper Greensand beds occur 
nnfossiliferons sandstones, in which thin coal-seams haye beea 
detected; and these are in turn ooyered by strata of chalk, converted 
into a silioeons rock, but still retaining in its casts of fossils (Belem^ 
nitella^ Inoeeramus^ Spandylus, &c.), and in its beantifnllj preserved 
microscopic organisms (Foraminiiera, XarUhidia, &c.) nnmistakable 
proofs of its age and the conditions of its deposition. Above iiiis 
representative of the highest member of the English Chalk there 
ooonr argillaceous strata with coal seams and plant-remains which 
are perhaps the eqidvalent of younger members of the Oretaoeons 
series, not elsewhere found in our islands ; or, it may be, they must 
be regarded as belonging to periods intermediate between the Ore* 
taceous and Tertiary epochs. It is greatly to be regretted that 
these Cretaceous deposits of the Western Highlands are so un- 
fiftvourably displayed for our study as to present scarcely any f acd- 
lities for the coUection of their fossils ; for these, if found, might he 
expected to throw a flood of light on some of the most obscnra 
palaeontological problems of the present day. 

Although the comparison and correlation of the Secondary strata 
of the Highlands with those of other areas, and the discussion of 
the questions of ancient Physical Geography thereby suggested, are 
reserved for the fourth and concluding part of his memoir, the 
author takes the opportunity of making reference, in bringing the 
present section of his work to a dose, to several problems on 
which the phenomena now described appear to throw important 
light. In opposition to a recent speculation, which would bring 
into actual continuity the present bed of the Atlantic and the old 
Chalk strata of our island, he points to the estuarine strata of 
the Hebrides as demonstrating the presence of land in that area 
during the Cretaceous epoch. He also remarks on the singular 
agreement of the conditions of deposition of both the Silurian and 
Cretaceous strata of the Scottish Highlands and those of the North- 
American continent. But he more especially insists on the proofs 
which we now have that the Highlands of Scotland, as well 
as the greater part of the remainder of the British Islands, were 
once covered by great deposits of Secondary strata, and that the 
area has been subjected to enormous and oft-repeated denudation. 
He dwells on the evidence of the vast quantities of material which 
have been removed subsequently to the Mesozoic and even to the 
Miocene period ; and he maintains the conclusion that many, if not 
all, of the great surface-features of the Highlands must have been 
produced during the very latest division of the Tertiary epoch, 
namely the Pliocene. 



Digitized by VjOOQIC 



[ 317 } 
XLV. Intelligence and Miscellaneous Articles. 

ON GALVANIC CURRENTS BETWEEN SOLUTIONS OF DIFFERENT 
DEGREES OF CONCENTRATION OF THE SAME SUBSTANCE, AND 
THEIR SERIES OF TENSIONS* BT DR. JAMES MOSER. 

T HE electromotive force of liquid galvanic series is influenced by 
the concentration of the liquids. In order to determine the 
OAture of this influence, I have investigated, in the laboratory of 
Professor Helmholtz, liquids with which it is possible to isolate 
this influence of the concentration. All chemical processes were 
to be excluded ; therefore only differences of concentration might 
exist or changes in it occur during the passage of the current, 
lakewise, for the elimination of all chemical actions, it was neces- 
sary that the electrodes should consist of that metal which waa 
contained in the solution. 

Two glasses with differently concentrated solutions of the same 
salt were connected by a siphon ; and the circuit was closed by a 
metallic conduction with the electrodes just mentioned. I then 
observed, in all the cases investigated^ that a current arises which 
proceeds from the more dilute to the mQre concentrated solution. It 
may be represented thus : — 

Zq, dilute Zn SO^, concentrated ZnSO^, Zn. 

This current appeared regularly in a series of solutions of sulphate, 
nitrate, diloride, and acetate oi zinc, sulphate and nitrate of copper, 
chloride of iron, acetate and nitrate of silver, &o. 

I observed the electromotive forces of these series by Poggen- 
dorff's method of compensation, modified by Du Bois-Eeymond, 
from a few thousandths up to one fifth of a Daniell, the latter force 
between very dilute and highly concentrated solutions of zinc 
chloride. 

I give, in the following Table, the ten electromotive forces, be- 
tween the combinations of two, of five solutions of sulphate of 
zinc, the unit being nearly 0*001 of a Daniell : — 



100 parts of solution contain of 
Zn80,+7H,0 


16 per 
cent. 


30 per 
cent. 


46 per 
cent. 


60 per 
cent. 


1 per cent. 
15 „ 
30 „ 
45 „ 


18 


22 
5 


28 
13 

7 


36 

21 

17 

9 



These numbers indicate a series of tensions ; for e. g. the electro- 
motive force between 

16- and 30-per-cent. solution is 6, 

30- and 60-per-cent. solution . . 17, 
16- and 60-per-cent. solution . . 21, 

I then confirmed the existence of a series of tensions by con- 
necting with each other, by four siphons, five glasses, of which the 
Ist, drd, and 6th contained solutions of equal strength (46-per- 
cent.), the 2nd contained stronger solution (60-per-cent.), the 

Digitized by VjOOQIC 



318 Intelliffence and JUiscellaneous Articles. 

4th weaker (15-per-eent.). I immened the one electrode in glaaa 1, 
the other sucoessiyely in 2, 3, 4, 5. When the second electrode 
dipped in 3 and 5 I obtained no current, because the concentra- 
tions of the terminal solutions were equal ; but on the inuneTsion 
of this electrode in gUss 2, and in 4, there was alwajs a deflection 
produced — ^in the one case by the electromotive force 9, between 
solutions of 45 and 60 per. cent., in the other by the force 13, in 
the opposite direction, between 45- and 15-per-cent. solutions. 

I made the same experiments on a series of other salts, and thus 
determined the 15 electromotive forces between the couples formed 
by six solutions of cupric sulphate : — 





B 


c 


D 


E 


F 


A 


10 


16 


21 


25 


27 


B 


, , 


6 


11 


16 


17 


C 


, , 


, , 


5 


9 


ll 


D 


, , 


, , 


, ^ 


4 


« 


B 


•• 


•• 


• • 


•• 


2 



E was a solution containing, in 100 parts, 30 of crystallized salt 
(GuS0^-f-5H,0). One hundred parts by volume of this solation 
were mixed in E with 33^, in D with 100, in G with 300, in B with 
700, in A with 2900 parts of water. 

By these currents, goinff from the diluted to the concentrated 
solution, metal is dissolved in the diluted, and separated from the 
concentrated solution. Only when the concentration is the same 
in both solutions does the current cease. 

for the work accomplished by the current we should have to seek 
the corresponding equivalent in the work of the force of attraction 
between the salt and the water, which makes itself perceptible in 
the thermal actions which can be observed on mixing different solu- 
tions of the same salt. 

Accordingly the current observed by me must be conceived as a 
reaction-current against the migration of the ions, as the polariza- 
tion-current is one of reaction against the decomposition-current ; 
for whenever any salt is electrolyzed, the solution becomes more 
concentrated at the anode, more dilute at the cathode. My expe- 
riments show that then arises an electromotive force which acta in 
opposition to that of the electrolyzing battery. — MoiuUt^>€ri(M der 
kon. preuss. AJcad, d. WiMensch, z, Berlin, Nov. 1877, pp. 674-676. 

ON THE EXTRACTION OP GALUUM. 
BT MM. LECOQ D£ BOISBAUDRAN AND £. JUKGFLEI8CH. 
The smallness of the quantity contained in the minerals in which 
galhum has hitherto been detected renders its preparation costly 
and tedious. We proposed to ourselves to pursue a process per- 
mitting this preparation to be annexed to that of a . commearcial 
product, and thence to operate on a manufacturing-scale, on con-* 
siderable masses. 

The realization of this project we owe to the support of M. L^n 

Digitized by VjOOQIC 



Intelligence and Miscellaneous Articles. 319 

Thomas, who has been anxious to oontribute, with generous liber- 
alitj, to the success of a research of pure science. M. Thomas has 
kindly had treated according to our directions 4300 kilograms of 
Bensberg bJende, that ore bSng the richest known. 
The course adqpted was as follows : — 

1. The blende, pulverized, is roasted in one of the bays of a 
Perret oven kept at a sufficiently high temperature by the simul- 
taneous combustion of pyrites in the other bays. The gallium re- 
mains fixed, while the greater part of the indium appears to be 
volatilized. 

2. The product of the roasting is treated with a quantity of sul- 
phuric add sufficient to dissolve nearly all the zinc, leaving never- 
theless in the mass enough subsulphate to cause the filtered solution 
to become cloudy on the addition of cold water. Thus, on the one 
hand, commercial sulphate of zinc is obtained, and, on the other, a 
residue containing gaJlium. 

3. This residue is again taken up by excess of sulphuric acid. 
After reduction of the persalt of iron by metallic zinc, the filtered 
liquor is precipitated by carbonate of soda (fractionating and fol- 
lowing the course of the operation with the spectroscope). The pre- 
cipitates are again taken up by sulphuric acid ; then a second reduc- 
tion ii effected with zinc, and a fractionation with carbonate of soda. 

At the Javel works all the gallium of the 4300 kilograms of blende 
was thus concentrated into a mass weighing (still wet) about 100 
kilograms. Tliis product was remitted to us by M. Thomas. At 
this point, indeed, the treatment ceased to be on the large scale, 
and could be pursued in a laboratory. 

4. To remove the iron, which, through reoxidation, in tolerably 
large quantity escaped the preceding purifications, the reductions 
by zinc and the mctionations by carbonate of soda are repeated 
several times. 

5. The galliferous- precipitates are again taken up by sulphuric 
add ; most of the excess of acid is eliminated by evaporation ; and 
the residue is boiled with a large quantity of water. The filter 
separates a deposit containing some titanic add. 

6. After purifying by sulphuretted hydrogen, to the very add 
liquor, still suffidently charged with zinc, acetate of ammonia is 
added, and it is again treated with hydrosulphuric gas : sulphide 
of zinc is predpitated, carrying with it some gallium, which is thus 
separated from the alumina. The additions of sulphate of zinc, 
acetate of ammonia, and the currents of hydrosulphuric add are 
repeated as long as the sulphide gives the gallium-lines. 

7. The sulphuric solution of the galliferous sulphides of zinc is 
carefully fractionated with carbonate of soda. Spectral examination 
assisting, a pretty accurate separation of the zinc is accomplished. 

8. After fresh treatment with sulphuric acid in the predse propor- 
tion necessary, we separate by sulphuretted hydrogen alittlecadmium , 
lead, indium, zinc, &c., then raise to ebullition the liquor diluted 
with much water. By filtering it while hot we collect a consider- 
able amount of subsalt of gallium, which is immediately washed with 
bcHling water ; for with cold it would redissolve in its mother-liquor. 

9. The basic salt is readily attacked by potass, which leaves in the 

Digitized by VjOOQIC 



320 Intdligence and Miscellaneous Articles, 

insoluble state some iron, indium, &c. The alkaline liquor, treated 
with hydrosulphuric gas, then slightly acidulated with sulphuric acid, 
gives a precipitate consisting principally of sulphide of indium*. 

10. The very slightly add liquid being boiled with a large quan- 
tity of water, the gallium passes again into the state of a subsislt. 

11. The gallium is isolated by electrolysis of the potassic solu- 
tion of the subsalt. The deposition of the metal is effected advan- 
tageously only under special conditions. The intensity of the 
electric current, for example, should vary according to the state o£ 
the liquor ; but the surface of the negative electrode must always 
be relatively small compared with that of the positive electrode. 
In one of our operations, which produced 8 grams of gallium in 
twenty-four hours, 40 Bunsen elements (18 centims. in height) 
arranged in eight parallel- series, each comprising 5 elements in 
tension, put in action a negative electrode the double surface of 
which did not exceed 15 square centimetres, while the positive 
electrode presented an expanse of about 450 centimetres square. 

The metal, when deposited cold, often forms long files of crystals 
resembling needles, normally fixed to the electrode by one ex- 
tremity ; some of them attained the length of 3 centims. Above 30^ 
the metal trickles in drops, which collect at the foot of the electrode. 

By operating in the manner above described, we collected 62 grams 
of crude gallium. If account be taken of the inevitable losses, and 
of some grams of gallium which still remain in our various pro- 
ducts, the content of the Bensberg blende may be estimated at ^oii) o* 
or nearly 16 milligrams per kilogram. This minute proportion of 
material capable of extraction accounts for the operations requiring 
so long a time. 

We purified the crude gallium by filtering it through linen of a 
close texture, agitating it in hot water acidified by hydrochloric 
acid, and repeatecQy crystallizinff it. From this we afterwards 
prepared the crystals, plates, and superfused mass of gallium which 
we nave the honour of presenting to the Academy. The little bar 
was cast with metal not refined. 

In an early communication we will recount various obsenations 
made in the course of our operations. — Comptes Rendus de VAca^ 
dSmie des Sciences, Feb. 18, 1878, tome Ixxxvi. pp. 475-478. 

ON THE RESISTANCE OF FLUIDS. 
To the Editors of the Philosophical Magazine and Journals 
Gektxjbmen, Berlin, S. W. Grossbeerenstr. 24, March 8, 1878. 

In your Magazine for December 1876, pages 434 and 435, Lord 
Bayleigh gives two formula (3 and 4) for the resistance of an 
elongated blade held vertically in a horizontal stream. These formole 
were given before Lord Eayleigh by myself, in a paper entitled 
" M. Thiesen, zur Theorie der Windstarke-Tafel, Sanct Petersburg, 
1875," Wild's Eep. f. Meteorologie^ J. iv. No. 9, p. 7. 
I am. Gentlemen, yours faithfully, 

Dr. M. Thiesew. 
* It must be remarked that indium is but partially precipitated by potass 
and by sulphide of potassium. 

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Figl. 




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Earth 










Fig. 5. ' \ 




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Fig G. 



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THE 
LONDON, EDINBURGH, akd DUBLIN 

PHILOSOPHICAL MAGAZINE 

AND 

JOURNAL OF SCIENCR 

— * — i>r»n{Auv 



[FIFTH SERIES.] , - v r x- l- o • r m. ,- 
MA Y 1878. < A 1^1 F( )RXIA. 



XL VI. On the Edge-angle and Spread of Liquids on Solid 
Bodies. By G. Quinckb*. 

[Plate XU.] 

1. JNTRODUCTIOK— In a former communication t I 
have investigated the phenomena of capillary action 
at the common surface of tw^o fluids, and have measured the 
oapillaiy constant, or tension, ai^^ of this common surface^ by 
various methods. 

The fluid particles themselves must be assumed to have a 
ready mobility, in order that the condition of equilibrium may 
be rapidly attained. This is, of course, only approximately 
the case. The more viscous the fluids considered, and the 
greater the friction of the fluid particles, either of the same 
fluid or of the different fluids, against one anoilier, the more 
slowly will the condition of eauilibrium be attained. The 
course of the phenomena may oe essentially modified from 
this cause. 

* Tranalated by Silvanos P. Thompson, from Poggendorifs Annalen. 
t Pogff. Ann, cxxxix. pp. 1-89 (1870) ; and PhU. Mag. [TV.'] vol. xli. 



No. 273 (April 1871). 

X [The subjoined extract from the memoir of 1871 referred to above 
explains the author's use of symbols. — ^Transl.] : — '^ In the following 
memoir I shall use the same notation as in my former communications on 
Capillary Phenomena (Pogg Ann, 1858-69y, and shall distinguish the 
magnitudes which relate to a point P,- or P, of the free surface of the 
liquid 1 or 2 by means of the sufHx 1 or 2, the magnitudes which relate 
to a point P, 3 of the common surface of two liquids 1 and 2 by means of 
the double suffix 1 2." 

Phil. Mag. S. 5. Vol. 5. No. 32. May 1878. Y 

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322 Prof. G. Qaincke on the Edge^ngU and 

Imagine several fluids in contact with one ano&er (for ex- 
ample a lenticular drop of water upon oil or mercary) and let 
them be gradually cooled down : tne water will finally freeze. 
The attraction between the particles of oil or mercair^ and the 
particles of the frozen drop of water will differ only by an in- 
considerable quantity from the attraction which they would 
have exercised upon the particles of the fluid drop of water. 
The common surface between the oil or mercury and the water 
will have similar properties whether the water be flaid or solid ; 
and in the common surface of oil and ice, or of mercory and 
ice, a surface-tension otis must exist similar to that in the com- 
mon surface of oil and water or of mercury and water. 

Moreover the ready mobility of the particles of oil or of mer- 
cury amonffst one another, and especially their mobility with 
respect to me now immovable particles of water, will probably 
have been changed. 

A similar consideration may be applied to other bodies in 
the liquid and solid conditions as to liquid and solid water ; 
and hence we arrive at the following universal proposition : — 

In tlie common bounding surface of afluvi 2, and of a solid 
body 1, there exists a surface-tension a^}, as in the camtnon 
boundary of two fluids. 

This surface-tension will be the same within the flaid and 
within the solid body, provided only the particles are imme- 
diately on the common (geometrical) boundary of both sub- 
stances. The surface-tension will be perceptible only under 
special circumstances in the solid body, whose particles are very 
difiicultly movable amongst one another, but more easily in 
the fluid layer which bounds the surface of the solid body. 

It might therefore be assumed, to return to the previously 
mentioned special case, that a capillary surface-tension existed 
not only in the capillary surface of the frozen drop of water 
bounded by mercury, but also in the free surface of the frozen 
drop bounded by air — ^a surface-tension which would have 
the same value for all points of the free surface, and which 
must be independent of its geometrical figure. 

The fluid layer at the common bounding surface of a solid 
body 1 and of a fluid 2 would therefore behave as a stretched 
membrane having at all points a constant surface-tension 

The action of the particles of the solid body upon a fluid 

i)article at the point r is such as if there acted in the free sar- 
ace of the solid body bounded by air, a constant surface-tension 
«i, independent of the geometrical figure of the surface, having 
the same value for every fluid particle P of the intersecting line 
of the capillary surface. 



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' spread of Liquids on Solid Bodies. 323 

The laws established formerly* by me, relative to the surface 
common to two or three fluids, may, if the foregoing consi- 
derations are just, be henceforth extended also to the case 
where one fluid is replaced by a solid body. 

Let the three common surfaces of a solid body 1 and of two 
fluids 2 and 3 intersect in a curved line ; then, upon a particle 
P in the intersecting line there act three forces lying in the 
plane normal to the element P of the curved line of intersec- 
tion under consideration. These forces are equal to the capil- 
lary constants or surface-tensions of the three capillary surfaces, 
and are in equilibrium ; consequently they fulfil the conditions 
of the equation 

sinwg sintTj sinu?! ^ ^ 

In this equation w^, t^jj, w^ represent the angles which are re- 
spectively subtended at the point P by the mutually intersect- 
ing elements of arc of the curved capillary surfaces whose 
directions coincide with the directions ox the forces ^13, ^3, ^3^. 
The symbol «i2 represents the surface-tension or capillary con- 
stant of the surface common to the solid body 1 and the fluid 
2, &c. 

If a triangle be drawn (Plate XII. fig. 5) whose three sides 
are proportional to the capillary constants or surface-tensions 
of the bounding surfaces common to the solid body 1 and to 
the fluids 2 and 3, and which meet in a point P, then the ex- 
terior angles of this triangle give, for this point P, the edge- 
angles of the surfaces considered. 

The triangle is possible, and has real exterior angles, only 
if the sum of two sides be greater than the third, or when 

«13<«81 + «33 (2) 

If this condition is not fulfilled, a spread of one of the fluids 
will take plaice upon the surface of the solid body. 

Let us call 0^ the acute edge-angle which the surface com- 
mon to the two fluids makes with the surface common to the 
solid and to fluid 3 ; then 

^^®^« — 9:r~:. — ^^ 

When the magnitudes agj, ^23, and eii^ are independent of the 
geometrical form of the surfaces, and depend only on the 
nature of the fluids 2 and 3 of the solid body, then the edge- 
angle 6^ is also independent of tlie geometrical position of tlte 

• Pogg. Am. cxxxix. pp. 68, 69 (1870). Phil. Mag. [IV.] vol ili. 
No. 276 (June 1871), pp. 464-476. 

Y2 



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324 Prof. G. Quincke on the Edge-Single and 

surfaces of the solid and of the fluids^ constant for all points of 
the intersecting line of tJie three bounding surfaces, and deter^ 
mined only hy the nature of the solid and of the fluids. 

Therefore the surface common to mercury and water or air, 
for example, makes the same edge-angle with the solid wall 
of a cylindrical glass tube as the surface of a drop of mercury 
in water or air makes with a flat glass plate on which it rests. 

The second known axiom of the capillary theory concerning 
the constancy of the edge-angle is only a special case of that 
just mentioned (viz. the case when fluid 3 is air), and was first 
deduced, we majr remark in passin^^, by Dr. Thomas Young*, 
from considerations similar to the Sregoing. 

If the fluids are brought, as is repeatedly the case, into con- 
tact with solids which have a continuously curved surface 
without sharp comers or edges, as, for example, into a glass 
tube or onto a flat plate, then the surface-tensions of the sur- 
faces common to the solid and to the fluids 2 and 3 act in op- 
position to each other. 

Let normals be drawn to the surface of the solid 1 and to 
the free surface of the fluid 2, and let the acute edge-angle 
which is included between the normals be called 0% ; then 
there is equilibrium as soon as the following equation is ful- 
filled:— 

«i8=«i8-t-«a8COs53; (4) 

or, omitting the index 3, 

^^e^^^irJ^ (5) 

(see Plate XII. fig. 6\ 

The edge-angle oecomes 0°, and the fluid spreads over 
the wall of the tube and moistens it, as soon as 

«1-"«12>*2 (6) 

For the case where the air is replaced by a fluid 3, the con- 
dition of spread is __ 

«18~"*13>«S3 (6 a) 

The theory developed in the preceding paragraphs will, in 
the sequel, be compared with experience. 

2. The edge-angle of the free surface of a fluid must be the 
same for flat air-bubbles under a level plate of glass as for fluids 
which ascend capillary tubes of the same material. 

From the whole height K, and from the vertical distance 
(K— A) between the horizontal and vertical elemente of the 

♦ I^ectures on Natural Philoaopby, ii. p. 668 (1807), and Young*a 
Works, i. p. 459 aeqq. {Encydop. Brit, 1816;, 



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Spread of Liquids on Solid Bodies. 325 

meridional curve of a bubble * of a fluid 2, of specific gravity 
<T, under a level glass plate, are found (subject to a small cor- 
rection dependent on the diameter of the bubble) the cohesion 
a and the edge-angle by the equations 



«=(K-*)«|, 



cos 2 = 



K J^ 



(7) 
(8) 



If we call A the mean ascent, and •& the edge-angle of the 
same fluid in a glass tube of radius r, then 



(») 



(10) 



(a) = «cosd=-^; . . . 

or, dividing equation (9) by equation (7), 

e, (a) rh 

If plates and tubes are made of the same sort of glass, the 
values of the edge-angles and ^ found from equations (8) 
and (10) must be equal. 

I have in a former communication t measured for equal 
times the heights of flat air-bubbles under a glass plate, and 
the elevation, in newly-drawn glass capillary tunes, for a series 
of simple liquids. They yield the following values of the edge- 
angle. 

Table I. 



liquid. 


Specific 
gnjity. 


Coliemon. 
a. 


Air- 
bubblea. 
Edgen 
9. 


OapiUary 
tubea. 
uigle. 


Water 


1 

0-9136 

1-2687 

0-7977 

1-4878 

0-8867 

0-7906 


mgr. 
8-253 
3-760 
3-274 
3-233 
3120 
3-033 
2-59& 


25 32 
21 50 
32 16 

36 20 

37 44 
25 12 


2§4^ 

29 34 

28 50 
24 14 

30 35 


Oliye-oil 


Biflulphide of carbon .. 

Petroleum 

Chloroform 


Oil of turpentine 

Alcohol 





* Compare with M. Quincke's paper in Pogg. Ann, cxxxix. (1870), and 

"" '' '"'" '^' 1871). 

Mag. [IV.] vol. xli. 



PhiL Mag. [IV.] vol. xli. No. 278, p. 249 (April 18 
t Pogg. Ann, cxxxix. p. 16 (ISf 0) ; and Phil. 
No. 273 (^April 1871), p. 252, 



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326 Prof. G. Quincke on tlie Edge-Single and 

Except in the case of bisulphide of carbon, where an impos- 
sible value of the edge-angle is found in the capillary tubes^ 
the values of the edge-angle as determined by both methods 
agree with each other. 

I obtained the same result with aqueous solutions of salts 
and with alcohol. For these I have combined, from innumer- 
able experiments, the mean values of the edge-angles for 
air-bubbles and ^ for capillary tubes in the last two columns 
of Table XI. of a previous communication*. These exhibit 
most discrepancy between 20° and 30°. 

Greater discrepancies between and d are shown only with 
solutions of KCl, MgClj, CUSO4, NaNOs, KNOs, and especi- 
ally of carbonate of potash. 

If these discrepancies might also have their origin in acci- 
dental impurities, it appeared to me nevertheless to be desirable, 
instead of these convenient estimations, to bring about direct 
measurements of the edge-angle, the more so as a much greater 
accuracy may be attained by the latter f. 

3. In order to measure directly the edge-angle 9, which the 
extreme portion of a free fluid surface makes with the level 
surface of a solid body, I employ the following method of 
reflexion: — ^A clean thread of glass (tubing), newly drawn out 
in a flame, is bent into a little siphon ; the ends are cut off with 
a clean file, and the siphon is placed in a glass which stands 
upon a clean horizontal plate of plate-glass, Gx. Pass a small 
spirit-flame below the bend of the siphon, and the limb of the 
siphon sets itself exactly vertical. 

If the glass be filled with a liquid, it climbs by capillary 
attraction up the glass thread as high as the bend ; and at the 
opening of the vertical tube of the siphon bounded by sharp 
edges (see fig. 1) drops are formed with clean surfaces. The 
volume of these drops is almost independent of the velocity 
with which the drops are formed, and is equal to half the 
specific cohesion a^ of the liquid in question multiplied by the 
periphery of the tube-wall on which the drop forms. 

In most cases the drops are formed on the outer wall of the 
siphon-tube, so that it is possible, by the selection of glass 
thi*eads of suitable internal and external diameters (usually 0'5 
to 1 millim.), to get drops of suitable size to follow one another 
at intervals of from about 1 to 30 seconds. By shifting the 

♦ Pogg. Ann. dx. pp. 371-374 (1877). 

t For mercury and transparent solid bodies the method of two reflexions 
formerly contrived by me is to be preferred (Poggr. Ann, cv. p. 40, 1668). 
The changes of the edge-angle observed at that time I think must chiefly 
be ascribed to the oil-yapours which expanded in the apparatus exhausted 
of air, as then used. 



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Spread of Liquids on Solid Bodies. 827 

horizontal glass plate under the sipbon-moath the drops may 
be caused to fall upon different places of the plate, so that the 
liquid forms shallow segments of spheres wim sharp circular 
edges. 

Fig. 1 shows the contrivance as it is used. Several liquids 
may at the same time form drops near one another. The un- 
used drops are caught by a square glass trough, upon the 
upper cut edge of which a small strip of plate-glass Gj is laid 
to serve as a table. This table is set exactly horizontal with a 
spirit-level and small wooden wedges. 

The glass plate with the drops is then placed upon a hori- 
zontal rectangular plate of plate-glass, near which is set a ver- 
tical divided circle, having a movable arm of light straw of 
350 millims. length and carrying a sight of black paper. On 
rotating the apparatus, the sight, which has an aperture of 2 
millims. diameter, describes a vertical circle, in the centre of 
which is the sharp edge of the drop. 

A luminous flame being placed at several metres distance, 
two images are formed by reflexion, at the level surface of the 
glass and at the curved surface of the drop, due to the reflect- 
ing ravs ARi and ARj (fig. 2). The first image is of 
natural size, the second smaller in proportion as the fluid sur- 
face is more curved. If the arm with the sight be turned 
forward beyond the line A B^ in which the last portion of the 
surface of the drop reflects the light, the little image of the 
flame suddenly disappears ; and this position is read off to the 
exact minute of arc, with a vernier, upon the vertical divided 
circle. The arm bearing the sight must be turned back through 
an angle 20 in order to receive the image of the flame reflected 
from the level surface of the plate. The last-named position is 
determined once for all, and onlv verifled as often as appears 
necessary ; so that a single reading sufiices to determine the 
edge-angle 6. 

The exactness of this first method admits of being easily 
further increased by the employment of a telescope ; yet 1 
have found the apparatus, in the simple form described, com- 
pletely adequate for my rather long-sighted eye, so long as 
values of 6 which do not exceed 40° are in question. 

For larger edge-angles, the method described has the disad- 
vantage that the flame-images in the strongly-curved surface 
of the drops are very small and, especiallj-^ in daylight, difficult 
to perceive. 

It is therefore more convenient to measure the edge-angle 
by a second method, with a simple goniometer of the following 
construction. 

Upon one side of a horizontal steel wire, AA^ (fig. 3) 



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828 Prof. G, Quincke on the Edge-^ngU and 

of 110 millims. length and 2 millims. diameter, is fastened 
with cork a mirror S (of silvered glass) of 30 millims. height 
and 15 millims. breadth, and upon the other side a vertical 
divided circle K, of 45 millims. diameter, printed on card and 
divided to whole degrees. An arm B C of the same steel wire 
serves to rotate the divided circle and mirror in a hole C D 
bored through a large cork which has been forced tightly onto 
a vertical glass rod G, of 250 millims. length and 8 millims. 
diameter. Two diametral arms of brass, M Mi, which are like- 
wise fastened into the large cork, allow the rotation to be read 
oflFtoO°-l. 

That the reflecting surface S stands parallel to the axis of 
rotation A Ai is verified, as in the ordinary goniometer, by- 
rotating through 180°. 

The mirror S must be placed horizontal and near to a larger, 
straight^dged, horizontal mirror G^, so that the images of a 
horizontal window-bar parallel to A Ai reflected in each mirror 
may coincide. Upon the horizontal mirror G9, and as near 
as possible to the mirror S, is laid the fixed plate with the flat 
drops whose edge-angle is to be determined, llie eye is 
lowered until the reflected image of the sky-lit window has 
just disappeared at the curved surface of the drop ; and the 
mirror S is turned about the axis A Ai until the upper edge 
of the bright image of the window appears on a level with the 
edge of the drop. Then the mirror stands parallel to the last 
element of the free surface of the drop, and the rotation frona 
the first position to the second, measured on the divided circle, 

S rives directly the acute edge-angle with a precision sufficient 
or the purpose in question. 

4. Influence of Height of Fall and of Impurities upon the 
Edge-angle, 

The ed^e-angle is found to be the smaller as the height h 
from whicn the drops fall upon the plate is greater. 

For water, and a glass nlate carefully cleansed with alcohol, 
water, and a clean linen cloth, I found : — 



A=0 millim. 
^=22° 34' 



20 millims. 
12° 44' 



130 millims. 
7° 13' 



With another plate of the same glass plate better cleansed : — 

AssO millim. ( 10 millims. I 100 millims. 
^=12° 29' I 9° 8' I 5° 54' 

And two minutes later, repeating the experiment on another 
spot of the same plate: — 

^=16^49' I 14° I 8° 41' 



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Spread of Liquids on Solid Bodies. 329 

When the glass was replaced by a silver plate (a mtrror-glass 
silvered by Martin's process) the values were: — 



A=0 millim. 
5=12° 49' 



50 millims. 
6^26' 



By AssO most be understood a fall of the least possible height. 

If the drop of water is left to evaporate^ or if a portion of 
the water be removed by a clean thread of ^lass, the drop be- 
comes thinner and the ed^e-angle smaller^ me surface of con- 
tact with the solid remainmg practicallv unchanged. 

When with greater heights of fall tJie drop becomes more 
flattened by striking upon the flat surface^ the same mass of 
fluid acquires a greater surface of contact with the solid. This 
surface of contact retains its original dimensions^ and is 
found too small. 

If fresh fluid is added to the drop, the surface of contact 
grows more slowly than the altitude of the drop, and the edge- 
angle acauires the same value as with minimum height of fall. 

The following measurements, when it is not expressly stated 
otherwise, refer always to the case of minimum height of fall 
or of maximum edge-angle. The size, and the velocity with 
which the falling drops follow one another, have only a slight 
influence upon the edge-angle. The deviations are at least not 
greater than are shown by similar drops upon the most homo- 
geneous surface possible, and seldom amount to more than 3(y. 

Accordingly I found when water was dropped from a wide 
or a narrow siphon tube upon a freshly-cleaned black glass : — 

5=6° ir or 5° 5y. 

After the glass had laid some time in the air: — 

5=24° 7' or 25° 15'. 

A clean thread of glass was cut in two, and of it two siphons 
bent, so that the drops formed themselves on the portions that 
were previously united. One siphon was drawn out longer 
and narrower at its middle point in a clean alcohol-flame so 
that 10 drops of water formed on it during a minute, while 
upon the otner 40 drops of almost the same size were formed 
in the same time. The edge-angle for white plate-glass then was 
7° 30^ or 6° 31', 

according to whether the drops fell slowly or quickly. 

The cleaner a surface is, other circumstances being equal, 
the less will the edge^ngle be found. 

A black glass plate cleansed with alcohol and a clean linen 
cloth showed for water the edge-angle 

7° 34'. 



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830 Prof. G. Quincke Ofi the Edge-angle and 

The ^lass - plate was rubbed with olive-oil and a clean linen 
cloth till all visible oil was removed ; the edge-angle of the 
same plate for water was now 

The drop of water was then after some minutes poared off, the 
last traces evaporated, and after deposition of a new drop with 
a less surface of contact the edge-angle was 

42° l(y; 

and on a repetition of the same operation, 

31° 53^ 

The glass surface behaved, therefore, like a quicksilver sur- 
face, upon which, as I have formerly shown in detail*, water 
has a greater or a smaller edge-angle, afkier it has been coated 
with nlm of foreign fluid more or less thick, provided the 
thickness of the mm is less than 2Z, or less than double the 
distance at which the molecular forces of capillarity are still 
operative (see § 12). 

In the researches here described, a portion of the film of oil 
with which the glass plate was coated dissolved in the water ; 
the thickness of the film became thereby less, and a freshly 
deposited drop of water showed a less edge-angle. 

Between the surfaces of the solid glass and the fluid mer- 
cury there obtains, however, the essential difference that the 
bounding surface common to water and mercury is easily dis- 
placeable, but that common to water and glass is very diffi- 
cultly movable. 

In the case of water and mercury, when the water is removed 
in portions, the normal edge-angle is forthwith restored ; iu 
the case of water and a solid, such as glass, the edge-angle 
becomes smaller. 

In the earlier researches with surfaces of mercury ty it waa 
possible, by applying very small quantities of oil to the free 
surface of the mercury or of the water, to diminish the tension 
of these surfaces and to give a lesser or a greater diameter to 
the drop of water, and a greater or a lesser value to its edge- 
angle. 

This experiment does not succeed in the case of drops of 
water upon glass or any other solid body. 

If the free surface of a drop of water freshly deposited upon 
a glass plate be touched with a glass thread moistened with oil, 
a portion of the oil spreads upon the free surface, but the edge- 

• Pogg, Am, cxxxix. pp. 66 & 78 (1870); and PhU. Mag. [IV.] 
vol. xli. pp. 874 & 460 (1871), 
t Pogg. Ann, cxxxix. p, 67 ; Phil Mag. [IVJ vol xU. /oe, eiU 



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Spread of Liquids on Solid Bodies. 331 

angle of the water against the glass remains almost unaltered. 
Should an alteration take place, it is sometimes positive, some- 
times negative, and seldom amounts to more than 1^. Con- 
sequently I could not detect anj change of the surface of 
contact of glass and water. 

5. Water behaves towards other solid bodies — quartz, calc- 
spar, mica, Ac. — similarly as towards glass. Here also the 
edge-angle is smaller as the surface of the solid body is cleaner. 

The surface of glass is never obtained clean by rubbing it 
witti a clean linen cloth and with alcohol, nor by longer im- 
mersions in alcohol. The best course is to treat the glass 
with hot concentrated sulphuric acid, wash this off with dis- 
tilled water, let it lie a considerable time in clean water to 
remove the last traces of acid, then take the plate with pla- 
tinum tongs and dry it in the warm current of air above the 
colourless flame of a Bunsen burner. 

The plates are allowed to cool upon a clean watch-glass in 
a large clean glass jar covered with a glass plate. 

There certainly remains after this process, at the edge of the 
last drop that dried up, a little of the glass which had been dis- 
solved in the water ; and this coating modifies the edge-angle. 

In a similar manner cut plates of quartz may be cleaned. 

In the case of selenite, mica, calc-spar, and topaz, fresh 
surfaces of cleavage are used. 

The acute edge-angle of water upon the substances men- 
tioned is generdly the greater the longer the time which has 
elapsed since the cleansing or the formation of the clean sur- 
face, during which the solid bodies condense upon their surface 
gases or vapours from the air*. Even a few seconds suffice 
to allow the influence, which always increases the edge-angle 
of the water, to become recognizable. Topaz appears to me 
most sensitive ; less sensitive are calc-spar, glass, selenite, mica, 
and quartz, which last substance keeps a clean surface the 
longest. 

Since I found it impossible to split the substance without 
touching it on the edge with the finger, the freshly cloven 
surfaces may probably in consequence have been also soiled. 

I have determined the edge-angle with the cleanest possible 
surfaces specially for water and olive-oil, and for water with a 
surface rubbed with olive-oil and a clean cloth, or greasy. 

The figures given are the mean of several measurements. 
Under " min. " are placed the smallest values which I have 
found in these measurements. 

• Rieffi has formerly remarked {BeibungselectrieUaty vol. ii. p. 220) that 
a drop of water remains Btationary upon an old surface of mica, but flows 
at once over a fresh one and wets it. 



Digitized by VjOOQIC 



332 



Prof. G. Quincke on the Ed^e^^ngle and 



Table II. 



1 


Edge-angle. 


1 
1 


WaU 
Clean surface. 


Br on 


Olire-oil on 
dean Burfaoa. 


Topas 


min. 

Ui 158 
4 15 2 24 
3 2 
2 8 1 22 
1 16 
55 



e 1 

80" 
18 1 
8 4 
12 39 

7 58 


i2 11 

47 3 

34 38 
17 29 
10 35 
24 24 


Oalc-BDar 

Black glasB 

Selenite i 


Mica 


Quartz ! 

Slate ' 


1 



A gold-leaf electroscope was immediately discharged on 
contact with the clean surfaces of topaz, calc-spar^ glass, mica, 
and quartz, but not discharged, or only very slowly, on con- 
tact with the greasy surfaces of the same substances. Plates 
of selenite wim either clean or greasy surfaces discharged the 
gold-leaf electroscope. 

6. Metals are still more difficult to obtain with a clean sur- 
face than glass or the substances named in the preceding 
parapraphs. 

Noble metals, as platinum and gold, in thin strips of 10 
millims. breadth, are ignited in the non-luminous Bunsen*s 
flame, and allowed to cool in a clean watch-glass between clean 
glass plates. 

For silver I employed a film of silver deposited upon clean 
plate-glass by Martin's process*, which was rinsed with water 
as hot as possible and dried in the warm air-current over the 
Bunsen-flame. 

Other metals were scraped with a clean knife, and the flat 
drops brought as quickly as possible onto the clean surfaces so 



After waiting a longer or shorter time T after the prepara- 
tion of the clean surface before depositing the flat drops of 
fluid, different values are always found lor the edge-angle. 
In the case of water and aqueous saline solutions the difference 
is specially astonishing ; it is less in the case of olive-oil. 

Pure alcohol and petroleum spread over a clean surface upon 
the whole of the metalsi nvestigated by me, and gave the edge- 
angle 0°. 

• Pogg. Ann. cxxix. p. 56 {ISi'JQ). 



Digitized by VjOOQIC 



Spread o/Liguidit on Solid Bodiei. 



333 



In the following Table are comprised the means of a series 
of measurements of water or olive-oil on the cleanest possible 
surfaces : — 

Table III. 
Edge-angle for Clean Surfaces. 



Clean surlkce of 


Watet. ' 


Olive-oil. 


Water with 

alcohol which 

spreads. 


T=2'. 


T=10'. 


Plntdimm 


O 1 

10 43 

4 16 

11 32 

6 41 
2 36 

5 10 

7 15 
5 52 

8 11 
4 40 


8 18 
17 58 


29 43 
33 47 
25 59 
23 15 
29 56 
27 33 
29 37 
33 28 
23 56 
35 48 


o , 1 

20 40 


Gold 


12 54 
18 25 

14 1 
17 45 

16 37 

13 42 

15 59 
7 42 


Silrer 


CoDuer 


lST......;;:...::. 


Iron 


Oadmium 

. Zinc 


I Aluminium 

' Pl&te-£la80 


1 ^""^^"^ 



When alcohol spreads upon the clean metal surface and 
drives away the water already lying upon it, the water drop is 
driven back ; but it remains bounded by a sharp edge, and its 
edge-angle is increased, as a comparison of the figures of the 
last column with those of the second shows. 

If the clean metal surface be smeared with a thin fihn of 
grease by rubbing with olive-oil and a clean cloth, the edge- 
angle of water or alcohol against the greasy surface is much 
greater than against the clean surface. Its magnitude depends 
on the thickness of the deposited film of oil. If the greasy 
surface be left some time in contact with alcohol, wherebv a 
portion of the oil-film is removed, and the alcohol be tten 
poured ofi* and the remainder evaporated, water shows a smaller 
edge-angle on that place with the thinner oil-film. 

If petroleum be smeared upon the clean metal instead of 
olive-oil, the water behaves towards the greasy metal surface 
as in the case of olive-oil. Alcohol spreads upon it and ex- 
hibits the edge-angle 0^. 



Digitized by VjOOQIC 



834 



Prof. G. Qaincke an the Edge-^ngle and 



Table IV. 
Edge-angle on Greasy Surfaces. 



Thick film upon 


Thin film ofl 
petroleum. 


Thin film of olive oil. 


Water upon 

the same sur- 

faoe treated 

with alcohol. 


Edge-angle for 
Al<x)hol. 1 Water. 


Edge-angle 
fop water. 


Plfttinum •••..•... 


6§ i 
88 

(80) 

(90) 
62 30 
37 36 
36 14 
47 42 

(95) 
15 10 


O i 

2t»33 
15 6 

14 5 
2<» IS 

18 14 

15 2i 

19 45 

19 15 

20 4 



44 25 
72 10 
54 48 
60 54 
>75 

(80) 
75 55 
31 


2§24 ! 


Oold 


44 52 i 


Silrer 


22 10 


CODDOP 


4 55 1 


LeT ..:::.::...". 




Iron 


1 


O&dmiuni ..**i... 


72 1 


Zino 


20 29 


Aluminium 

Plate-glass 





If once a metallic surface come into contact with oil, the 
adherent film of oil cannot be removed either by washing with 
alcohol or by immersion for a day in that fluid. The edge- 
angle of water against the greasy surface always remains ma- 
terially greater than is yielded by the clean or fresh surfaces. 

The thinner the film of oil upon the surface of the solid bod^r, 
the less will be found the edge-angles of alcohol and water 
against the surface in question. 

7. Aqueous saline solutions behave similarly to water in 
spreading upon clean plate-glass. 

The following Table contains the means of a series of obser- 
vations upon saline solutions of various degrees of concentra- 
tion : — 

Table V. 

Edge-angle for Plate-Glass, and Aqueous Saline Solutions of 
various degrees of Concentration. 





Specific 


Amount of 




Substance. 


grayity. 


salt. 


Edge-angle. 




9, 


S. 


9. 


Hydrochloric add 


1 
10655 



1455 


% 9 
3 53 


' 


I 





4 15 


Chloride of ammonium .. 


10365 


1330 


9 3 




10737 


35^8 


12 42 


CaUoride of sodium 


1 
10865 



1327 


3 9 
6 11 




] 





8 59 


Chloride of potassium ... 


10487 


808 


8 2 


^ 


10932 


1613 


12 16 



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Spread of Liquids on Solid Bodies, 
Table (continued^ 



335 



SabnUnoe. 



Cfhloride of OAlciam . 



Snlphnrio aioid 



Sulphate of lino 



Sulphate of copper .... 
Oarbonate of potaarium .. < 



Nitric aoad.. 



Nitrate of potanium . . . 
Ammonia , 



Oane-sugar 



Spedfio 
grayity. 



1 

lld89 

1 

1-0556 

1*2318 

1*3470 

1-5197 

1-8371 

1 

10910 

12187 

14168 

1 

10664 

M859 

14444 
1 

10110 
1-0915 

11398 

?• 
1 

11170 
1*2359 



Amount of 
tolt. 

B. 




28*01 



8*48 
4514 
85*61 
1611 
180-4 



9*28 
22-59 
45*88 



6*40 
19*64 


72-63 



2-20 
18-08 



25*80 
? 


37*67 
102-20 



Edge-angle. 
9. 



i36 
15 48 
6 
485 

4 37 

4 21 

5 4 

6 1 
4 25 
9 6 

15 7 
20 26 

4 38 
10 54 
12 1 

730 
14 81 

4 38 

5 30 

6 69 

5 6 

6 37 
0<> to 7<> 18' 

6 24 

7 8 
9 2 



I obtained similar results for other solid bodies^ as platinam 
or gold : — 

Table VI. 



Fluid. 


Specific 
gravity. 


Bdge-angle. 


Glass. 


Platinum. 


Gold. 


Water 


1 

11639 

1-4444 


?3<i 
15 48 
14 31 


I si 

15 17 
8 37 


8 11 
7 45 

7 8 


Chloride of calcium 

Oarbonate of potaaeium.. 



According to these researches the edge-angle appears to 
increase a little with an augmenting concentraHon of the saline 
Bolntiony but otherwise to differ only inconsiderably from the 
edge-«ngle of pure water. 

S. Besides the direct methods described in the preceding 
paragraphs^ I have also simultaneously determined the edge-* 
angle indirectly aminst the same solid sqbst((uce9 from the 
form of flat air-bubbles. 



Digitized by VjOOQIC 



336 Prof. G. Quincke on the Edge-^ngle and 

Upon the same surfaces of fflass and silver, which were 
cleansed with alcohol, water, and a clean linen cloth, I foond 
by both methods the following values of the edge-angle for 
mixtures of alcolwl and water of various specific gravities: — 

Table VII. 



Alcohol of 
specific 
grayity. 


With air-bahbles. 


Bj reflexion. 


Glass. 1 Silrer. 


OUss. 


SilTer. ! 


0*9973 
09859 
09200 


30 53 43 31 
96 93 1 69 18 
16 91 90 91 


90 34 
15 36 
14 98 


7§U 
69 35 
95 49 



With the exception of the one determination in the case of 
very dilute alcohol and silver, where the fluid surface of the 
air-bubble was ver}*^ difficultly movable, and a casual impurity 
may have produced a difference, the results of both methods 
of observation agree as far as can in general be expected in 
these investigations. 

9. The magnitude of the surface-pension ui^ at the boundary 
of a solid and of a liquid may be determined to within an ad- 
ditive constant so soon as the tension of the free surface, and 
the edge-angle for various liquids upon the same solid (for ex- 
ample glass), are known. 

From equation (5), § 1, we have for the fluids 2 and 3 : — 



or, by subtraction, 



ax2=ai — Ascos^s, 



«lJ'~«18 = *8COs5j — OjCOS^j. 



(5a) 
(5b) 

(5 c) 



Call h the mean height of ascent in capillary tubes of dia- 
meter 2r for a liquid of specific gravity <r ; then, from equa- 
tion (9), 

a^ cos 0^ = (a) ^rh^j 

whence follows at once the capillary constant (a) of the free 
surface of the liquid concerned, as it used formerly to be cal- 
culated from the height of capillary ascent in glass tubes under 
the assumption that 3ie edge-angle was zero. 

Moreover the value of a^ cos 0^ may also be calculated from 
observations on flat air-bubbles beneath a level plate of glass. 

Comparing au for various liquids with 

«1B = « 



Digitized by VjOOQIC 



Spread of Liquids on Solid Bodies. 337 

for water as fluid 3, we obtain the following values from my 



earlier observations * : — 



Table VIII. 



liquid. 


SpeciOc 
gntTity. 


*iCO«^i = «i-«ia- 


SurfaoA-teiiBion 
agaizust glass. 


Capillarj 
tubes. 


Air- 
bubbles. 


Capillary 
tubes. 


Air- 
bubbles. 


Alcohol 


07906 
07977 
1-4878 
0-8867 
0-9136 
1-2687 
1 
13-543 


mgr. 
2-:f37 
2-566 
2-733 
2-765 
3271 
3-343 
7235 


mgr. 
2^2 
2-604 

2-398 
3-490 
2-768 
7-419 
34-53 


mgr. 
4-998 
4-669 
4-502 
.4-470 
3-964 
3-892 



mgr. 
6097 
4-845 

3959 
4-681 

-27081 


Petroleain 


Chloroform 


Tnrn*ntin© 


OliTe-oil 


Bisulphide of carbon ... 

Water 

Mercury 



In this Table the liquids are arranged according to the value 
of their surface-tension at the boundary of glass, as follows 
from the observations upon capillary tubes. 

With the exception of mercury, the bounding-surface of glass 
and alcohol exhibits the greatest, and that of glass and water 
the smallest surface-tension. Instead of which we may also 
say alcohol has the least, water the greatest adhesion to glassf. 

A similar calculation may be carried out in the case of all 
the aqueous saline solutions for which I have lately t established 
the values of «. According to equation (5 c), in the case of all 
saline solutions for which (a) increases with augmented con- 
centration, the surface-tension of the common bounding surface 
of glass and saline solution will be the less, and the adhesion 
of the saline solution to the glass will be ihe greater, as the 
saline solution is the more concentrated. This occurs for all 
the substances investigated by me, with the exception of hy- 
drochloric acid, nitric acid, and ammonia ; and it holds also for 
alcoholic solutions of chloride of lithium and chloride of cal- 
ciam§. Besides, the same quantity a^s may be calculated in 



♦ P 
No. 27J 



Ann. czxzix. p. 15 (1870) ; and Phil. Mag. [IV.] vol. xli. 
XNO. x/o {April 1871). 

t For melted glass I have found (Pogg. Ann. cxxxv. p. 642, 1868) 
«(jS 18*09 mgr.; and since this value was necessarily obtained with a 
lowering temperature^ there is nothing astonishing in the value «j>-d4*6d, 
as follows from equation (5 a) and the obeervations on mercurv. Accord- 
ing to this equation, «, must always he greater than a value of a.cos^. 

t Pogg. Ann. clx. pp. 371-874 (1877), table xi. § Zoe. eti^ p. 566. 

P/itf. Mag. S- 5. Vol. 5. No. 32. Mat/ 1878. Z 



Digitized by VjOOQIC 



(5d) 



99 



338 On the Spread of Liquids an Solid Bodies. 

yet anotlier way from the obserration of flat babbles or drops 
of one liquid 2 in another liqaid 3 or 4, beneath or upon a 
glass plate. 

From equation (4), 

«lJ = «18 + «S8COS(98, .... 
«1S = «14 + «S4 008^4; 

or^ by subtraction^ 

ai4— «1J = «J8 COS ^j—«S4 008^4. 

Let the flat glass correspond to the solid I, 

olive-oil „' „ liqaid ... 2, 

waner j^ m» >■ . . • o 

alcohol yy jy ,, ••• 4 ; 

tiien according to my earlier observations*, 

0,8=2-096 mgr., «,4=0-226 mgn, 

^8=17% ^4 =87^48', 

«i4-ai8=2-001 mgr. -0-009 mgr.; 

or if the boundary of glass and water ai8 is called Xy 

«i4—a?«B 1*992 mgr. 

According to this investigation also, the surface-tension of the 
level bounding surface of glass and alcohol is therefore greater 
than that of glass and water. 

If water be taken as fluid 3, and the various liquids of ob- 
servations Nos. 2, 10-14, & 16 of the former researches men- 
tionedty as fluid 2, then the surface-tension of the common 
boundary of glass and the liquid concerned may be calculated 
from equation (5d), except an additive constant «i8, or a. 

Tablb IX. 



Bounding lurfaoe of glass 
with 


Surface-tension with 
glass. 


Bisulphide of carbon ... 
Pfttrolftum It.** 


2815 
2001 
1-992 
0931 

-3823 


Olire-oii 


Alcohol 


Turpentine • 


Water 


Meroury.«*...««. .....t— .t* 





The figures of the last columns in both Tables VIII. and IX. 

• Pogg. Arm, cxzxix. p. 27 (1870) ; and Phil. Mag. [IV.] vol. xli. 
p. 263 (April 1871). t Il>id. 



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On Thermoelectric Currents in Strained Wires. 339 

shoald be identical ; likewise the order of saocession of the 
liqaids. 

Neither is the case ; and so far the theory is not in harmony 
^th experience. 

It most, indeed^ be remembered that the values of the edge- 
angle ^ were only determined approximately with flat babbles 
and drops, and can lay no claim to great accuracy — ^that the 
magnitude «| of the free surface of the glass may have had 
diflSrent values in the various researches in consequence of 
impurities (see § 12, hereafter) — and, finally, that merely the 
presence of a fluid may alter the molecular nature and therefore 
also the surface-tension of another, so that the density of a 
snrface bounded by air may be quite different from that of one 
bounded by another fluid (compare § 11). 
[To be continued.] 

XL VII. TIte Production of Thermoelectric Currents in Wires 
subjected to MecJuinical Strain, By G. W. VON TuNZEL- 
MANN, Holder of the Clothujorkers* JExhibition in Chemistry, 
and Physics at University College, London *. 

THE following inquiry was suggested by some observa^ 
tions recorded in a paper of Sir William Thomson's on 
the Electrodynamic Qualities of Metals, in the * Philosophical 
Transactions ' for 1856 ; and the object in view was to investi- 
gate the conditions under Vhich thermoelectric currents are 
produced in a circuit composed of a single metal when one 
portion of the metallic conductor is subjected to a strain and 
the junctions of the strained and unstrained portions are main- 
fained at difierent temperatures. 

The experiments were made upon wires of iron, steel, and 
copper, the copper wire employed having been obtained from 
Messrs. Johnson, Matthey a Go. as chemically pure. 

Two tin cans were obtained open at the top, and pierced at 
the bottom by necks into which india-rubber corks were in- 
serted ; and through slits in these the wires were passed. The 
wire was fastened by a clamp in the lower can, ana was grasped 
in the upper one by a pair of wire-drawing dogs attached to 
the shorter arm of a lever, to the longer arm of which was 
attached the weight by which the strain was produced. In 
the earlier experiments ordinary weights were used ; but ulti- 
mately these were rejected, as it was found impossible to apply 
and remove them in a sufficiently gradual manner to prevent 
a certain amount of shock, which introduced complications. 



Communicated by the Physical Society. 
Z2 



Digitized by VjOOQIC 



340 Von Tanzelmann on ttie Production of TliermoeUctric 

In the arrangement finally adopted^ there was attached to 
the longer arm of the lever a tin can open at the top^ and 
having at the bottom a neck fitted with an india-mbber tube, 
which coald be closed by merely bending it np and hitching 
it in a hook attached to me can for that parpose. The strain 
on the wire was then produced as gradually as was desired, by 
pouring in measured quantities of shot ; and it could be removed 
as gradually by letting the shot run out by the india-rubber 
tube. 

The two cans through which the wire passed were filled with 
water, the water in the upper can being kept at the temperature 
of 100° C. by means of a gas-burner, while that in the lower 
can could be kept for a considerable time at a uniform tempe- 
rature by allowing a current of water, of the same temperature 
as the place of experiment, to circulate through it. 

The extremities of the experimental wire were bent round 
in a large curve and brought close together; they were then 
tied to me extremities of two covered copper wires connected, 
through a four-way key, with a Thomson's galvanometer 
having a resistance of between one and two ohms. The junc- 
tions were then placed side by side separated by thin paper, 
and wrapped up in cotton-wool, as was done by Thomson in 
his experiments, to prevent the production of currents by the 
unequal heating of the two junctions. 

Before being used the wires were annealed : — the iron and 
^teel wires by being heated to redness in an iron tube, through 
which a current of coal-gas was passing to prevent oxidation; 
the coppep wire by being slowly passed through a Bunsen 
fiame, as it was found that the exposure of the copper at a red 
heat to the current of coal-gas produced an efiect similar to 
that known as over-poling in the process of refining copper, 
the wire being rendered so brittle as to break with the least 
strain. 

Thomson found in his experiments that when a weight was 
applied so as to produce a state of strain in a portion of the 
wire, and the two junctions of strained and unstrained por- 
tions were kept at different temperatures, in iron and steel 
wire a current was produced the direction of which was from 
the unstrained to the strained portion across the hot iunction, 
while in copper wire the current was in the opposite direction* 
When the weight was removed the result was in either case 
a M'eaker current in the reverse direction. 

Some experiments of the same nature have also been made 
by M. le Boux, and described in the Annales de Chimie et de 
Physique^ 4th series, vol. x. p. 201 (1867). He obtained 
results of the same nature as Thomson — with the notable 



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Currents in Wires subjected to Mechanical Strain* 34 1 

difference that in iron and steel wires he got a current from 
strained to unstrained across the hot junction, while in copper 
wire the current was from unstrained to strained across the 
hot junction. On comparing the descriptions of the experi- 
ments, it appeared that Thomson had always made his expe- 
riments with comparatively small strains, while Le Roux had 
strained his wires very nearly to the breaking limit. This at 
once suggested a possible explanation of the apparent discre- 
pancy between their results ; and on making the experiments, 
it was found that as the strain was gradually increased the 
current was increased, as in Thomson s experiments, but only 
up to a certain limit. When the strain was increased beyond 
this limit there was a gradual decrease in the current; and if 
the strain was very carefully increased, the direction of the 
current was reversed shortly before the breaking strain was 
reached. 

During the experiments, it was very soon observed that after 
a weight had been added the current did not remain constant, 
but gradually diminished ; while at the same time there were 
variations of small period in the strength of the current, which 
were greater when the weight was added suddenly, and scarcely 
perceptible when it was very carefully and slowly added by 
pouring in shot; these variations gradually ceased when the 
apparatus was not disturbed. A very gentle and gradual ad- 
dition of weight diminished these variations, which always died 
away more rapidly when there was a heavy strain on the wire. 
Clutching the wire in the " dogs '* also set up these variations, 
which were allowed to subside before beginning the experiment. 
These results suggested that the production of the current 
might be due to a process of change in the molecular state of 
the wire ; it was found, however, on examination that there 
was a permanent effect which could not, as far as I can see, 
be produced in that way, whatever may have caused the tem- 
ponuT effect. 

Where the results obtained at different times had not to be 
compared, the current is generally given in terms of the de- 
flections of the galvanometer ; but where such comparison was 
necessary, the value of the deflections was determined at each 
experiment in terms of a standard current obtained by send- 
ing a current from a Daniell's cell through a definite resist- 
ance. 

For the sake of brevity, U.S. will be written for " from un- 
strained to strained across the hot junction;" and the oppo- 
site direction of the current will be denoted by S.U. The 
following letters are used in the description of the experi- 
ments: — 



Digitized by VjOOQIC 



342 Von Tanzelmann on the Production of Thermoelectric 

W = tension applied to wire in pounds^ = 3 times weight 

actually applied to lever ; 
M = number of measures of shot effective in stretching 

wire, = 3 times Jiumber actually applied to lever ; 
B = temperature of lower can ; 
D = mean deflection of galvanometer ; 
C = strength of current in terms of the standard current. 

A considerable number of preliminary experiments were 
made to verify Thomson's results and to determine the best 
form of apparatus, the arrangement ultimately adopted being 
that already described. These experiments (whicn are not 
described here) gave a general idea of the phenomena to be 
looked for. The alteration of resistance from strain is not 
taken into consideration, as H. Tomlinson's experiments, Proc, 
Roy. Soc. 1876 (vol. xxv. p. 451), have shown that it is too 
small to have an appreciable influence upon the results. 

Experiment 1. — An iron wire "46 millim. diameter. = 
16°; W = 31'5. The result is given in the accompanying 
Table, the direction of the current being U.S., the first read- 
ing being taken immediately after the weight was applied. 
It will be observed that the current does not reach its full 
strength immediately upon the application of the weight, but 
rises rapidly to a maximum, ana then gradually falls to a 
strength at which it remains steady. 

Time j. 

(minutes). 

2-5 

5 6 

10 3 

15 2 

20 2 

25 2 

Experiment 2. — A similar wire. 6=16°. The readings 
were taken immediately after the application of the weight. 
The sign * means that there is a deflection, bat too small to 
be measured. 

W. D. Directioii. 

6 * U.S. 

9 5 U.S. 

12 3-5 U.S. 

15 3. U.S. 

18 * S.U. 

21 -f "^^^ 

\ broke. 



Digitized by VjOOQlC 



Currents in Wires subjected to Mechanical Strain. 343 

It will be observed that the direction of the current changes 
jnst before the wire breaks. 

Some steel wire was now taken ; and as it was found almost 
impossible by the most careful annealing to get a piece of wire 
arranged in the apparatus which should give no deflection 
before the application of the weighty the initial deflection was 
noted in eacn case. 

Experiment 3. — A steel wire '81 millim. diameter. ©=:16°. 
Initial deflection = 20 S.U. W = 31-5. After the application 
of the weight the deflection reversed its direction to U.S. The 
result is given in the following Table. 

Time j. 
(minutes). 

2 10 

3 12 

4 13 

5 15 

6 18 

24 10 

25 9 

50 9 

90 5 

130 3 

The apparatus was then left for about 90 hours with the 
weight attached ; 6 being still 16^^ there was now a deflection 
of 15 S.U. The weight was then removed, and the deflection 
fell rapidly and changed to U.S. The subsequent deflections 
were as follows: — 

Time from removal D. 

of strain (minutes). U.S. 

1 2 

2 3 

3 4 

4 6 

5 7 

6 8 

14 8 

20 10 

25 7 

30 3 

In both cases we observe that the current gradually rises to 
a maximum and then falls. 

Experiment 4. — ^A steel wire '98 millim. diameter. = 15°, 
Initial deflection ss 10 S.U. On the addition of a weight of 



Digitized by VjOOQIC 



344 Von Tunzelmann on the Production of Thermoelectric 

42 lbs., the deflection changed rapidly to 14 U.S., and in abont 
an honr fell to 8 U.S., and in 40 hoars to 3 U.S. 

Experiment 5. — ^A steel wire '6 millim. diameter. 0=13^. 
Initial deflection = about 1 U.S. W=63 lbs. Direction of 
current after application of weight U.S. The weight was now 
left suspended for about 40 hours; but the apparatus received 
an accidental jar before the permanent deflection could be asoer* 
tained. The weight was tnen removed, causing a deflection 
of 8 S.U., graduallv increasing to 11, and then decreasing 
much more slowly than it had increased. 

Time from removal jv 

of Btrain (minutes). 

3 3-5 

6 4-5 

9 3-5 

12 2-5 

15 1-5. 

18 -87 

36 .... . * 

The efiect of rapidly putting on and taking ofi* the weight 
a number of times in succession was then tried; and it whs 
found that each time the weight was put on the deflection 
diminished, while each time that it was taken ofl^ the deflection 
was increased up to a certain limit. The immediate increase pro- 
duced by taking ofi^the weight was greater than the immediate 
decrease produced by putting it on ; so that on the whole there 
was a large increase in the current, the deflection being got 
up in this way to nearly 30 S.U., falling again very rapidly 
if the weight were left attached to the wire. Under these cir- 
cumstances the deflection went down rapidly to zero, changed 
sign, rose to a maximum, and then again began to diminish, 
passed through zero in the opposite direction, and so continued 
to perform excursions in alternate directions, and very rapidly 
decreasing in extent. When the weight was permanently- 
removed the deflection of the galvanometer died out much 
more slowly, and the changes of sign were only just percep- 
tible. These phenomena confirm the conclusion to which I 
was led by the fonner experiments, that there is, besides the 
main efiect, a transient effect produced by altering the strain 
on the wire ; and this transient effect appears to me to be due 
to the molecular state of the wire making a partial return after 
the first shock towards its primary condition, just as the im- 
mediate deflection of a spring suddenly stretched by a weight 
is greater than when it has come to rest in its position of equi- 
librium. The changes of sign in the current as it gradually 



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Currents in Wires subjected to Mechanical Strain, 845 

comes to its final state after the wire has been yiolently dis- 
turbed^ as in the last experiment, as also the fact of there being 
a permanent as well as a temporary effect, seem to render this 
hypothesis more probable than that the current is actnally 
prodnced by a change in the molecular state of the wire. 
The phenomena obtained in the last experiment will be ren- 

dArnd mnrA rHaur bv si. Hiftcrrnm- ^^ y 






The intervals between takinjg off and putting on the weight 
were approximately equal. ^Hiese are therefore represented 
by equal distances along the axis T; and the strength of the 
current is set off along the axis C. Starting from the point 
0, at the beginning ofthe experiment, with the weight attached 
to the wire as it had been left, then at any time the broken line 
represents the permanent change in the current pro- 
duced by taking off or putting on the weight ; 

represents the temporary change ; 

represents the resultant strengui of the current, being 

tlie sum of these two components. 

The curve A represents the change in the current when the 
weight is left permanently attached; and the curve A' repre- 
sents the change in the current when the weight is perma- 
nently removed. 

At this stage in the experiments the method of measuring 
the current-strength in terms of a standard current was adopted. 

The battery used as a standard was a " sawdust " DanieU's 
(Menotti's) cell; and the strength of the current was approxi- 
mately that produced by 1 volt through 10,000,000 ohms, or? 



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346 Von TuDzelmann on the Production of Thermodedrie 

10*"* C.G.S. unit. The measurements of the Tables are given 
in milliontfas of a C.G.S. unit. 

Experiment 6. — ^A similar steel wire. ©=16°. Initial de- 
flection barely perceptible S.U. Weight of 30 lbs. left on 
about 40 hours. 

It was observed that at the time of making the experiment 
the weight was making small oscillations; and this appeared 
to be the cause of tiie deflections making small oscillations 
about a mean value. At the end of an hour and a half the 
oscillations of the weight and also of the deflection had ceased, 
the latter remaining steady at 5, indicating a current '007 
U.S. The weight was now made to perform vibrations of 
small amplitude, upon which the oscillations of the deflection 
were greatly increased both in number and amplitude, and 
the mean deflection was at the same time somewhat increased. 
If the vibration of the weight be suddenly stopped, it is some 
little time before a decrease is perceived in the oscillations of 
the deflection. 

After setting the weight in gentle vibration, the effect in 
causing oscillations in the deflection was observable in less 
than a minute. If the vibrations of the weight are kept up 
for some time, the mean deflection is increased up to a certain 
limit, as before described. If the vibrations of the weight are 
increased in amplitude, the oscillations of the deflection become 
much more irregular, and the limits of variation become 
greater. 

Experiment 7 . — A similar wire. 0=12. Initial current '00 14 
U.S. A weight of 3 lbs. was now attached ; and at the end of 
two minutes there was a current *0052 S.U., falling at the 
end of an hour and a half to '0034 U.S. The weight was then 
increased by 3 lbs. at a time and the deflections taken immedi- 
ately, with the results given in the accompanying Table: — 

W, C. Directdon. 

6 -0038 U.S. 

9 -0019 U.S. 

12 -0014 U.S. 

15 -0012 U.S. 

18 -0012 U.S. 

21 -0012 U.S. 

24 -0012 U.S. 

27 -0010 U.S. 

30 '0002 U.S. 

33 ic S.U, 

In the experiments after this the weights are given in temia 
of measures of shot, each of which weighed about 7480 grains. 



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CurrerUa in Wires subjected to Mechanical Strain. 347 

Experiment 8. — ^A similar wire. 33 measures left on for 
abont 40 hours. B= 12°. Deflections read immediately after 
remoYal of weight. Direction of current S.U. There was no 
initial deflection. 

M. 0. 

33 -0095 

30 -0046 

27 -0035 

28 -0039 

21 -0049 

18 -0060 

15 -0067 

12 -0074 

9 -0084 

6 -0091 

3 -0098 

-0105 

Experiment 9. — A similar wire. 0=12°. No initial deflec- 
tion. Deflections read immediately after application of weight. 

M. C. DiTection. 

3 -0025 U.S. 

6 -0025 U.S. 

9 .... . -0021 U.S. 

12 -0014 U.S. 

15 -0014 U.S. 

18 -0014 U.S. 

21 -0014 U.S. 

24 -0014 U.S. 

27 -0011 U.S. 

30 -0007 U.S. 

33 -0004 S.U. 

36 -0014 S.U. 

Experiment 10. — ^A steel wire *47 millim. diameter. = 12°. 
Initial deflection 4 U.S. On attaching the empty can for 
containing the shot to the end of the lever the deflection in- 
creased to 20 U.S., falling to 14'5. The strain was gradually 
increased by pouring shot into the can until the wire broke. 
The deflecuon changed very little until the wire began to 
stretch, when the deflection fell very rapidly, passed through 
zero, and went up to about 40 S.U. 

The more rapid the stretching the stronger is the current 
produced. When the strain was slightly lessened, so as to stop 
the stretching, the deflection fell very quickly to 20 S.U. On 
removing the strain the deflection fell rapidly, passed through 



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848 Prof, Heluiholtz on Galvanic Currents 

zevoy and went np to 2 or 3 U.S., making irregular vibrations. 
The weight was replaced and additional shot ponred in very 
slowly. The deflection almost instantaneooslj changed to 
abont 2 S.U.; which increased slightly until the wire broke. 

Eaperimentll, — ^A copper wire '24 mil lim. diameter, ©as 15°. 
Initial deflection 1 S.U. 

M. D. 

1 

3 1 

6 3 

9 8 

12 3 

15 4 

18 4 

21 2-5 

24 2-5 

27 2 

30 1-5 

83 1-5 

36 1-5 

39 1-5 

42 15 

The direction of the current was S.U. Several small weights 
were added to the can ; but the deflection remained steady at 
1*5. In copper wire, no fall in the deflection was observed 
when the weight was left suspended for some time. 

The Physical Laboratory^ 
Universi^ College^ London. 

XLVIIl. On Galvanic Currents occasioned hy Differences of 
Concentration — Inferences from the Meclianical Theory of 
Heat. By Professor Helmholtz*. 

WE will regard as the electro-chemical equivalent of an 
ion that amount of it which is separated at the corre- 
sponding electrode, in the unit of time, by the chosen unit of 
current. 

The transport-number n, referred to the cation (Hittorf 's -), 

gives, as with Wiedemann, that fraction of the equivalent of 
tne cation in question which is carried by the unit of current, 
during the unit of time, through each cross section of the cur- 
rent's path in the solution, to the cathode. On the other hand, 
the quantity (1— n) of the anion goes in the opposite direction, 

• Translated from the Monatsbericht der Tcomglich preusaitchen Aho" 
demie^er Wmenschaften su BerVny Nov. 1877, pp. 713-726. 



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occ€uioned by Differences of Coficentratum. • 349 

by which (1— n) of the cation at the cathode becomes free — 
which, combined with the amount n of cation brought to this 
side, gives the quantity 1 set free at the cathode. In like 
manner the quantity n of the cation is conveyed away from the 
other side, by which n of the anion is set free. To this is added 
(1 — n) of the anion brought over. Now, when the cation is a 
metal which can deposit itself on the electrode, (1— n) of the 
metal disappears there from the solution, and (1— n) of the 
salt-forming acid is conveyed away ; consequently from there 
(1 — n) of the salt is removed. On the other side the liberated 
anion combines with the metal of the electrode ; and therefore 
1 equivalent of new metal here enters the solution, while n of 
the metal is carried away and (1— n) of the anion is brought 
over. This gives here an increase of the quantity of the salt 
by (1— n) of the equivalent for the unit of time and unit of 
current. If the metal of the electrode is the same as that 
which is contained in the solution, the total result of the elec- 
trolysis is the same as if one equivalent of metal were carried 
from the anode to the cathode, and (l^n) equivalent of salt 
in the solution from the cathode to the anode. 

If, then, the salt-solution is more concentrated at the cathode 
than at the anode, the difference of concentration is equalized 
by the transfer. Therewith the liquid approaches the state of 
equilibrium to which the forces of attraction between the water 
and salt tend even in the processes of difiusion, namely the 
state of uniform distribution of the salt. Thus the chemical 
forces acting in this direction will also in turn assist the elec« 
trie current acting in their direction. 

That the work of the chemical forces which herewith comes 
in acts in this case as an electromotive force according to the 
same lav/s as other electrolytic chemical processes, can be de- 
duced from the mechanical theory of heat. 

A reversible process without cnanffes of temperature, such 
as is required for the application of Camot's law, we can in- 
stitute in the following manner:-— 

(I) We let the quantity B of positive electricity slowly enter 
the anode in a constant current, and in return take away the 
quantity +E from the cathode; or, what leads to the same 
result, we admit + i B into the anode, and, inversely, discharge 
— ^E at the cathode. If Pj^ and P^ are the values of the elec- 
trostatic-potential function for the two electrodes, then is 

the work which must be done in order to brin^ about this 
through-current. If the duration of the current is equal to ^, 
the current-intensity according to electrostatic measure is given 
by the equation J< = E . 

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350 • Prof. Helmholtz on Galvanic Currents 

(2) Under the inflaence of this throagh-carrent, in the elec- 
trolytic cell, which we suppose provided with two electrodes 
of the same kind of metal and filled with a solution of that 
metal, there is brought about a transfer of the salt in the elec- 
trolyte. The alteration hereby produced in the state of the 
liquid we can get rid of by evaporating, from all the layers of 
the Uquid where the current attenuates the liquid, as much 
water as is conveyed thither, and, conversely, where the cur- 
rent produces concentration, introducing the corresponding 
amount of water by precipitation of vapour. If in this way 
the state within the liquid be maintained perfectly constant, 
the anion must remain wholly in its own place, because at 
neither end is any thing withdrawn from it, and nothing is 
added to it. From the cation, on the contrary, an amount 
perfectly equivalent to the current^intensity must pass through 
each cross section of the path of the current, since a full equi- 
valent is dissolved at the anode, and precipitated at the cathode. 
Now, since the displacement of the anion against the water is 
to that of the cation against the water as (I — n) : n, the water 
must move forwards with a velocity amounting to (1— n) of 
that of the cation. Consequently, if 1 electrolytic equivalent 
of the salt is combined with q parts by weight of water, and 
through a portion dm of the surface the current of density t is 
to be Ted, and, expressed in equivalents, the quantity idM of 
the cation, then must ;(1— n)i.c{oy parts by weight of water 
pass through the same in order to keep the parts of the anode 
m their place. 

This quantity of water, amounting to g(l— n)t.d«, carries 
with it as dissolved constituents (l—n)t.cf» equivalents of the 
cation as well as of the anion. Electrolysis impels through 
the same cross section ni.dm of the cation forwards, and 
(1 — n)i . do) of the anion backwards ; hence, on the whole, one 
equivalent of the cation goes forwards, and the anion remains 
in its place. 

Therefore, if u, v, w denote the components of the electric 
flow parallel to «, y, z^ reckoned according to the quantity of 
electricity which paases the unit of surface in the unit of time, 
the increase in the amount of water in the volume-element d4P, 
dtfj dz is, according to known hydrostatic laws, for the unit of 
time, 



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occasioned hjf Differences of Concentration. 351 

since in the stationary current 

|H + |«+|!f=o (lA) 

o^ oy oz 

On the contrary, at the surface of the electrodes the required 
inflow of water through the surface-element do) would be 

5(1— n)[tt cos a + r cost + ?r cos c]dc», • . . (1b) 

if a, h^ c denote the angles between the normal, directed to the 
liquid, of the element do> and the positive coordinate-axes. 

Integrating over the entire volume of the liquid the above 
expression which is multiplied by dxj dy^ dzy we obtain, by 
known methods of partial integration, the same value that the 
last expression (multiplied by d<o) gives when integrated over 
the surface. 

The water, then, which collects in the whole interior, and, 
according to our supposition, is to be removed by evaporation, 
will exactly suffice, when again precipitated at the smfaces of 
the electroides, to give the supply required there. Of course the 
collection of the water within the liquid, as well as its preci- 
pitation on the surface, may in places have also negative values. 

(3) The evaporation, or, where it is negative, the preqipita- 
tion of the vapour, can be managed thus : — By conveying heat 
to each of the volume-elements the temperature is kept con- 
stant during the evaporation. As long as water is to be ex- 
tracted from a volume-element of the liquid, the vapour is left 
in contact with it ; finally the two are separated, and the vapour, 
under a further supply of heat, is permitted to expand at con- 
stant temperature until it has reached a constant pressure pi. 
Where the evaporation is to be negative, of course the vapour 
is withdrawn from the pressure j?i, and giving up heat at con- 
stant temperature is compressed at first out of, and afterwards 
in, contact with the liquid, until it turns to water. Since the 
vapour which is in contact with the more concentrated por- 
tions of the liquid has less pressure than that which is in con- 
tact with the more dilute portions, work will be gained in this 
evaporation when water is carried over from the more dilute 
to the more concentrated portions, lost when the reverse is the 
case. 

(4) The electric current can be made to pass so slowlv that 
the heat-development (proportional to the square of its mten- 
sity) on account of the resistance of the conductor becomes 
vanishingly little in comparison with those actions which we 
have hitherto discussed, and which are proportional to the first 
power of the intensity. 

In like manner the difFusion which takes place between the 



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352 Prof. Helmholtz on GcUwinie CurrerUe 

differently concentrated portions of the solution ooald be 
duoed to a minimum by inserting narrow connecting tabes, 
without altering the electromotive force of the apparatus, which 
we wish to calculate. 

We can, on account of this^ neglect these two irreversible 
processes, and apply Camot and Clausius's law to the reversible 
ones. Since alt the bodies taking part in the process are each 
to have the same constant temperature, no heat can be converted 
into work, nor can any work be converted by the reversible 
processes into heat. The sum of the work gained and lost 
must therefore, taken by itself, be equal to nt7, as must also 
the sum of the heat withdrawn and supplied. Hence result 
two equations. 

The one, which refers to the heat, expresses nothing bat 
what can be obtidned without consideration of the electrolytic 
process — ^namelv, that the same amount of heat is generated 
when the metal of the electrodes comes into a concentrated 
sallHsolution which is gradually diluted as when it enters 
directly into the dilute solution. 

The second equation expresses that with the above-described 
reversible process the mechanical work must be equal u> nil. 
Work is expended, partly, 

(1) for the collection of the electricity. If P. and P^ are | 
the values of the potential-function in the anode and cathode, ! 
and in the time t the electricity H-E is collected in P. and ' 
taken out of P^, the work for the unit of time is, as already 
remarked, 

5(p.-p,)=j(p.-p,). ^ 

(2) Partly, work is performed by the expanding vapour. 
This vapour is first evolved under tne pressure », which cor- 
responds to the degree of saturation of tne liquia with salt; it 
then expands at a constant temperature up to the pressure pi. 
Naming the work for the unit of mass W, and the volume of 
the unit of mass Y , both referred to the given constant tern- 
perature, i 

W=pV+4 p.dv (Ic) 

The total quantity of this work, 2B, is found, by means of I 
the values shown in equations (1) and (1b) of the current, to | 
be equal to | 

-j'JJrfx.dy.rf..w{«^[9(l-«)] + i.|^[?(l-n)]+»|^[y(l-n)jj 
— f J(».Wg(l— n){MCOsa + rcosft + ircosc}=2B. (2) | 



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occasioned by Differences of Concentration. 353 

By partial integration of the triple integral, and taking into 
aooount equation (Ia), we find 

aJ=j'JJ«to.dy,&.g.(l-«)[«|^+r^^+«,^3^|(2A) 

Here n and W are functions of q. Consequently, if we put 

9(l-n)dW=d*, (2b) 

where «I> denotes a function of q^ or 

*=£?(l-")^di', (2c) 

in which /?, the pressure of the vapour above the salt-solution, 
is likewise a function of q^ we get 

20=:— j*A».*{ucosa + t?cos6 + u?cosc}. . (2d) 

The parenthesis in this expression denotes the component of 
the current perpendicular to the limiting surface of the elec- 
trolyte. Tins oifFers from nil only at the parts of the limiting 
surface turned to the electrodes. If the concentration of the 
liquid, and therefore q, u, p, ^, along each single electrode is 
constant, then becomes 

2B=J(4»»-4».), (3) 

and the equation of the work becomes 

P»-P.=^.-«>t=J^Vl-«)^- • . (3a) 

But Pj— P. is the value of the electromotive force produced 
by the electrolytic cell in the direction from the anode to the 
cathode, consequently in the direction of our assumed current. 

This equation therefore indicates the existence of an electro- 
motive force, the amount of which depends only on the con- 
centration of the liquid at the two electrodes, not upon the 
distribution of more concentrated and more diluted layers in 
the interior of the liquid — a conclusion which is confirmed by 
the experiments of Dr. J. Moser, recently communicated to 
the Academy. 

At the temperature of the apartment, the diminution of 
pressure shown by the vapour over the solutions of most of 
the metallic salts is very inconsiderable ; and on this account 

the quantity ^— may be supposed approximately constant 

within these narrow limits of the pressure. It can therefore be 
placed before the symbol of integration. On the other hand, 
Phil. Muff. S. 5. Vol. 5. No. 32. May 1878. 2 A 

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354 Prof. Helmholtz an Galvanic Currents 

according to Wiillner's experiments the diminution of the 
vapour-pressnre is to the amount of salt dissolved in the con- 
stant quantity of water directly, and therefore to our q in- 
versely proportional. If we use /?o? liitherto left undefined, 
to denote the vapour-pressure of pure water at the tempera- 
ture of the experiment, we may put 

Po-P'^-y W 

where b denotes a constant depending on the kind of the salt. 
Consequently 

P,-P.=6^f'''(l-n)-^. . . (4A) 
^P Jpt Po-P 

In intervals in which (1— n) has a constant value this would 
become 

P.-P.=Kl-")^loggE^ . . (4.) 

=Ki-»)f i<.g(^;) (4c) 

The quantity ^^— , here occurring, has at all events a positive 

value. If we suppose Mariotte's law valid for the inconsider- 
able densities possessed by the aqueous vapour at the tempe- 
rature of the apartment, and if V denotes the volume of the 
mass-unit of the vapour under the pressure p^ then (as noted 
above in equation 1 c) is 

According to Mariotte's law, 

p 

^ Pt 
I M=V,i)ilog(^), 

W=i>xVx{l+log^}, 
as an approximately correct value. 



(4PJ 



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occasioned by Differences of Concentration. 



355 



Hence it follows that the electromotive force of the cell is 
positive if the liquid is more concentrated at the cathode and 
consequently y*<^o and ^t<^«, which is likewise confirmed 
by a great number of observations by Dr. J. Moser. 

For inconsiderable concentrations^ and correspondingly slight 
diminutions of the pressure of vapour above the solution, for- 
mnlse (4 c) and (4 d) give also the law of the increase of elec- 
tromotive force toith rising conc^n^ra^ion of the solution, since 
the value of (1— n) is, according to Hittorf's investigations, 
nearly constant for slight concentrations, but rises for greater 
ones. 

The S of the following Tables is the quantity of water (pro- 
portional to q) which is combined with the anhydrous salt in 
the solution ; A is the electromotive force, according to the 
observations of J. Moser, stated in thousandth parts of a 
Daniell element (Cu, CUSO4, ZnSO^, Zn). The quantity 

1, S* 
^-jlogg^ 

a 

should, according to equation (4 c), be constant. 

For a cell with sulphate-of-copper solution and copper elec- 
trodes the foUowing values are found. 

Sulphate of Copper. 



Sit. 


Sa. 


A 

obeeired. 


A 

calculated. 


•?• 


Value of 1-n 
according to Hittorf. 


128-5 


4-208 
6-352 
8-496 
17-07 
34-22 


27 
25 
21 
16 
10 


27 

23-75 

21-45 

15-94 

10-45 


0-0550 
0-0552 
0-0562 
0-0548 
0-0575 


0-724 for S- 6-35 
0-644 for S>39-67 



As calculated values of A those are given which are obtained 
when the value of q from the first observation is retained for 
the others also. With sulphate and chloride of zinc, which 
can be employed in more concentrated solutions, greater 
deviations in these values occur* simultaneously with great 
increase in the values of (1 — n), 

* Note added Jan, 1878. — ^More recent experiments by Dr. Moser Bhow, 

indeed, that with zinc chloride the quantity --— = V increases to half as 

op 
much aj^n with greater concentrations, and can no longer be regarded as 
approximately constant 

2A2 



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356 Prof. Helmholtz on Galvanic Currents 

Sulphate of Zinc. 



s*. 


Bo. 


A 


A 




Value of l-n 


obeerved. 




«!• 


aixsording to Hittorf . 


163 


1-972 


36 


29 


0-0543 




.« 


2-963 


28 


26-4 


0-0635 


0778 for S= 2-524 





4-944 


22 


2S-1 


0-0707 


0-760 for S« 4-052 


— 


10-889 


18 


180 


0K)673 


0-636 for 8=26716 


^ 




Chloride of Zinc. 


99 


19 


21-5 


24-7 


0-0333 


0-70 for 8=332-87 





9 


40-4 


360 


0-0258 




— 


6-66 


42-9 


429 


0-0290 







2-33 


671 


66-2 


0-0243 


1-08 for 8- 2-774 





1-22 


120-9 


65-9 


00158 




— 


067 


200-0 




0-0108 





The great deviations which occur, especially with the higher 
concentrations, may probably be accounted for partly by the 
rise in the value oi (1— n) for the denser solutions, and partly 
by the more considerable diminution of the vapour-pressure. 
As the laws of both alterations for these salts have not yet 
been investigated, I could not institute a more detailed calcu- 
lation. 

Respecting the calculation of the absolute value of the electro^ 
motive force we have further to remark as follows : — ^The cur- 
rent-intensity J hitherto used is measured electrostatically; 
likewise the electromotive force P*— Po is determined in elec- 
trostatic units. Measured in electromagnetic measure the 
current intensitv J will become 

and the electromotive force 

9i=e(p»-p.), 

where Q is the velocity determined by W. Weber. According 
to the determinations of Friedrich ^Veber the electromotive 
force of a Daniell's element (Cu, CuSO^, ZnS04, Zn) is, in 
electromagnetic measure, 

Now W. Weber's electromagnetic current-unit, the unit of 
which is 

y/milligr. millim. _Q^Q^\/gram centim. 
second second ' 



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occasioned hy Differences of Concentration, 357 

decomposes, according to R. Bunsen, 0*0092705 mgr. of water 

159*5 
and -Jo— times as mach sulphate of copper — that is, 

0*082147 mgr. 

If, then, as in the numerical Tables, we denote by S the 
amount of water contained with one part by weight of anhy- 
drous salt in the solution, for the experiments with sulphate of 
copper 

(gq : 8=0-0082147 sec. a /-^^^^ : 1. 
V centim. 

Now, if the diminution of the vapour-pressure by the salt- 
solution employed is known, we obtain the constant b from 
the equation 

(iq 

in which the pressure p is also to be reckoned in absolute 

- jiram 

force-measure as — fj «• 

centmi. sec/ 

Our equation (4 c) becomes 

5l=e(P»-PJ=(gi).V(l-n)Iog(|!). 

Consequently the value of the constant ® need not be known 
for the calculation of the Si's in electromagnetic measure. 

Since we have assumed for the vapour the validity of Ma- 
riotte's law, the product 

The ratio ^ — - is, from Wiillner's experiments, in many salts 

nearly constant with changed temperature ; while the product 
2?o 'Vo increases approximately in proportion to the absolute 
temperature, which, within the limits of the temperature of 
the apartment, is not of much consequence. In fact the ex- 
periments do not show any considerable influence of the tem- 
perature upon the electromotive force of the cells ; at least it 
by no means varies in so great a proportion as the pressure of 
the saturated vapour. 

For testing the accordance of the absolute value of the elec- 
tromotive force of our series with that given by the formula, 
sufficient data on the vapour-tension of the salt-solutions used 
are still wanting. If we employ equation (4 c) in order to 
calculate, from the electromotive force found by J. Moser for 



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358 Mr. B. Mallet an the Sate of 

cells with sulphate-of-copper solutions, the quantity ^ — £ for 

the one-per-cent. solution at 20° C, we find this quantity 
equal to 0*00082; while M. Wulber* has found the same 
quantity, 

ForcanMugar =0-00070, 

For nitrate of potass... =0*00229, 
For sulphate of soda... =0-00236. 

From the chemical properties of sulphate of copper it is pro- 
bable that, in this respect, it takes its place between cane-sugar 
and the alkali-salts f. Experiments are in preparation in the 
laboratory here for the purpose of obtaining more accurate 
determinations. Meanwhile this calculation shows already at 
least so much, that the consideration instituted gives a theoretic 
value of the electromotive force which is of the same order of 
ma^itude as the observed. 

Since, moreover, factors obtained from the most various kinds 
of physical investigations, and one of which amounts to above 
a hundred millions, must be eliminated from both sides of the 
equation, this preliminary result is still of some importance. 



XLIX. Rate of Earthqxiahe^wave Transit. 
By R. Mallet, F.R.S,X 

I PRESUME that I have been indebted to the politeness 
of Greneral Abbot, U.S. Engineers, for a copy of a paper 
by that officer, published in the 'American Journal of Science' 
for March 1878. In this paper the writer recurs to his ac- 
count of the experiments made at Hallet^s Point on the occa- 
sion of the great explosion there, on the rate of seismic-wave 
transmission as described in General Abbot's paper read before 
the American National Academy of Sciences, October 18, 
1876, and also published as one of the papers of the Essayons 
Club of the Corps of U.S. Engineers. Upon the results there 
recorded I deemed it necessary to publish some remarks in the 
Philosophical Magazine for October 1877, in which I pointed 
out their anomalous character and their entire discordance 
with each other. If I rightly gather Greneral Abbot's meaning 
from his last paper above alluded to, he considers that the 

♦ PoggendorflTs Atmalen, vol. ciii. p. 656. 

t Supplementary Note (Jan. 1878). — Dr. J. Moser has since efFected 
determinations of the quantity in question, employing water and dilute 
solutions instead of mercury. He obtained 0'00086 as the mean value 
from three experiments. 

t Conmiunicated hy the Axithor. 



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Earthquake^wave Transit. 359 

enormous discrepancies between the results of observations 
made at different points along the range from Hallet's Point 
are reconcilable by taking into acconnt the difference in mag- 
nifying-power of the different seismoscopes there employed. 
It seems to me, however, that this proposed explanation, if 
critically examined, would be found wholly insufficient to 
account for the enormous discrepancies between the observa- 
tions made at the several stations, still less to reconcile the 
transit-velocities recorded with the well-established and inter- 
dependent physical conditions of the transit of sound, or ana- 
logous elastic waves, in liquids and solids. 

Few physical data have been better estabUsfaed experimen- 
tally than tbe rate of traoBit of sound in water (approximately 
about 4700 feet per second), as determined by Oolladon and 
Sturm in the Lake of Gteneva, and confirmed by Wertheim by 
a different method. Yet the transit-velocity in discontinuous 
waterrlogged shingle is given by observation No. 5 at 5309 
feet per second; and it is suggested that the rate is increased 
by the presence of the water. How these conditions are re- 
concilable with each other, or with the well-known physical 
conditions by ^hich the circumstances of transmission of 
sound are interdependent and linked together, I am unable to 
imagine. The proposed smoothing-down of the discrepancies 
by referring them to the differences in magnifying- power of 
t£e seismoscopes employed is insufficient to account for dis- 
crepancies so enormous ; and the proposed explanation seems 
to me only to amount to this — ^that if different observers note 
the instant of arrival as indicated by different parts of the same 
seismoscopic wave, they will necessarily obtain discordant 
results, and such as, in my judgment, no ingenuity of discus- 
sion of the observations recorded can reduce to the position of 
reliable scientific data. 

It is with surprise and disappointment that I find General 
Abbot has not acquainted himself with the magniiying-power 
of the seismoscope constructed by me and employed in all 
my experiments; and so little does he seem to have ac- 
quainted himself with the scientific literature of the subject 
before he himself commenced to work upon it at Hallet's 
Point, that I am compelled to suppose my published de- 
scription of that instrument, and all my earlier researches, 
which were not communicated to the Royal Society, but were 
published by the British Association for the Advancement of 
Science, remain even now unknown to him. My seismoscope, 
which is that which I have employed in all my subsequent 
researches, (reneral Abbot will find described by referring to 
my " Second Report on the Facts of Earthquake Phenomena," 



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360 Mr. R. Mallet on the Sate of 

printed in the British-Association Reports for 1851, and ac- 
companied by an engraving (plate 13) of the instrament. 
The circumstances are the more extraordinary, because my seis- 
moscope and its magnifying-power are also actually described 
in the account of my experiments made in the rocks of Holy- 
head, printed in the * Philosophical Transactions ' for 1861, with 
whidi General Abbot seems to have been acquainted. He 
will there find also, at page 279, that the magnifying-power 
of my instrument is 22*78, or nearly 23 times ; and this de- 
gree of magnifying-power I have found sufficient under all 
circumstances. I may notice, however, that in some experi- 
ments made a few years since hj me, at the desire of Sir 6. 
B. Airy, Astronomer Royal, of Greenwich, in concert with the 
then chief assistant of that observatory, Mr. E. J. Stone, now 
Astronomer at the Cape of Good Hope, and with Mr. Car- 
penter, one of the Greenwich computers, a seismoscope iden- 
tical in principle with my own, but of much greater magnifying- 
Eower, was employed, the power being capable of momfication 
y changing eyepieces. Any determination of wave-transit 
velocities was beside our object; but this was remarked di- 
stinctly, that changing the magnifying-power of the in- 
strument produced no noticeable change in transit-velocity as 
indicated oy it ; nor was any such, I believe, noticed by the 
late Sir James South in his experiments, made many years 
ago, to determine the extreme radius of the area caused to 
vibrate by railway trains passing through KUsby tunnel. In 
all these instances, however (except possibly that of Sir James 
South, as to which I possess no details), the seismoscope was 
used in the only way by which it can afford trustwortny and 
comparable results as to the instant of transit of the seismic 
wave as seen in the instrument, namely by bringing the hori- 
zontal wires of the illuminating achromatic object-glass parallel 
and near to the horizontal wire of the observing-telescope, and 
always noting and adopting as the instant of wave-transit the 
instant at which the image of both these wires became rapidly 
blurred or confused and suddenly invisible. This method, 
which does not seem to have been adopted in any of the Hal- 
let's-Point observations, is greatly to be preferred over any 
supposed observation of the earliest access to view of the front 
slope of the advancing wave, which, in reference to time, must 
always be a matter of great uncertainty. As to the duration 
of the vibratory disturbance in the field of view of the instru- 
ment, to which importance seems to have been attached in the 
Hallet's-Point experiments, it is quite delusive as affording 
any precise or useful information as to the dimensions or tinie 
occupied in the transit of the earth-wave or wave of shock 



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Eartliqxuike^wave Transit. 361 

itself — the duration of sensible disturbanbe as seen in the in- 
stroment being much dependent upon the dimensions, fonn, 
material; and other details of constmction of the mercnry- 
trough and other parts of the instrument. All the observa- 
tions of velocity of wave-transit referred to by General Abbot 
were made in completely discontinuoas material, or in rock 
more or less water-logged, and with the directions of stratifi- 
cation, lamination, and fissuring imperfectly known and not 
recorded. 

If General Abbot will refer to my experiments at Holy- 
head (Phil. Trans. 1861 & 1862), he wiU find the enormous 
retardation of transit-velocity prcxluced by fissuring and dis- 
continuiiv, amounting in some instances to an extinction of ^ 
of the velocity in the material of the rock if perfectly unfis- 
snred. The velociiy of wave-transit, therefore, in absolutely 
discontinuous shingle can be but a small fraction of that which 
the material of the shingle itself could transmit. General 
Abbot may satisfy himself of this by experiment upon this 
shingle by methods altogether indenendent of the use of the 
seismoscope. The velocity recorded in observation No. 5 — 
5309 feet per second (Amer. Joum. p. 179), cannot, as it 
seems to me, have been derived from the discontinuous shingle, 
and seems more likely to be an over-ratedvelocity of the wave 
derived from the water itself. Yet the velocities supposed to 
be obtained approach, in most instances, those ^ven as the 
results recorded by the greatest experimental physicists for 
the velocities of sound in media as uniform, dense, and elastic 
as are many metals. If General Abbot will consult the works 
of Wertheim, of Biot, not to name other renowned phvsicists, 
and will compare the Sound-velocities in solids as given by 
them with those recorded in relation to the Hallet's-Point 
experiments, I think he will see grave reason for doubt, at 
least, as to tibe validity of the latter. To me, indeed, it seems 
that, if they are to be accepted without further and radical 
modification or explanation, we must cast aside nearly all that 
has been accepted and is still held true as to the doctrine of 
sound by all men of science since the time of Newton ; we 
must also cast aside the deductions, as to the rate of transit of 
earthquake-shock, derived from observation by Professors 
Schmidt and Noggerath in earthquakes extending over large 
areas in Hungary and in Bhenish Germany, as well as those 
by myself of the great Neapolitan shock of 1857. Omitting 
the last^ as the time-measures were not free from doubt in 
some instances, those of Schmidt and Noggerath may be relied 
upon as made with much care and exactitude. All these 
results square as nearly as was to be expected with those of 



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362 Prof. P. E. Chase an the NOular Ht/pothesis. 

my own experimentallj obtained velocities in yarioos rocks 
lonff previously obtained, but appear to me wholly irrecon- 
cilable with those assumed as resulting from the Hallet's- 
Point observations. Is this probable? or is it not much more 
likely that some grave and still undiscovered sources of fallacy 
and error exist in these experiments, on which I have felt it 
incumbent on me thus to animadvert? 

Physical infinnity has prevented my examining the subject 
with that fulness I could have desired ; loss of sight has com- 
pelled me to confine myself to placing before Greneral Abbot, 
and scientific men in general, some of the difficulties which 
his Hallet's-Point experiments present to me and, I must 
suppose, to all competent phjsicisiB. 

L. On the Nebular HyvothesU. — ^VIII. Criteria. By Pliny 
Earlb Chase, LL.l).y S.P,A.S.y Professor of Philosophy 
in Haverford College. 

[Continued from p. 297.] 

THE views of astronomers, respecting the mode of action 
in world-building, have been various and vague. No 
one appears to have put upon record any numerical calcula- 
tions, undertaken with a view crucially to test the nebular 
hypothesis, or any suggestions as to the proper way to make 
such calculations. 

Statements have been made, at different times, by investi- 

S gators who thought that observed velocities might be explain^ 
f the results of nebular condensation ; but no one, except 
nnis*, has given us any means of judging on what grounds 
the belief rested. It seems likely tLat they all looked upon 
the formation of planetary rings as a merely superficial phe- 
nomenon, that their studies were limited to the direct action 
of living forces, that they used no adequate criteria for distin- 

guishing between nebular and meteoric influences, and that 
leir methods often, if not always, virtually assmned the very 
principles which they sought to prove. 

Herschelt, somewhat oDSCurely, intimated the possibility 
that nuclei might b^ simultaneously formed at different depths 
within the body of the nebula, by the action of particles of 
different densities; Peirce, Alexander, Hill, Wright, Kirk- 
wood, and myself discovered various planetary harmonies 
which point unmistakably to such synchronous internal and 
external activities; yet no one seems to have thought of 
the likelihood that interior portions would acquire a greater 

• * Oriffin of the Stare ' ; and Phil. Mag, April 1877, pp. 262-271. 
t Outlines of Astronomy, §§ 871-2. 



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Prof. P. E. Chase on the Nebular Hypothesis. 363 

aogalar velocifytiban the nebular nucleus, so that a planet might 
revolye in less time than its sun rotated, or a satellite in less 
time than its primary, until I called attention to the fact that 
the time of nucleal rotation must vary as the f power of the 
time of superficial nebular revolution. 

The significance of this relation does not seem, even now, to 
be generally understood ; for when Professor Hall found the 
unpjecedented rapidity with which the inner satellite of Mars 
actoally revolves, some thought that he must have made a 
mistake in his calculations, and others assumed that the dis- 
covery was fatal to the nebular hypothesis. It may therefore 
be a fitting time for an explicit statement of some obvious evi- 
dences of present nebular activity, such as are shown in the 
following comparative synopsis: — 



M~ 


n 


n« 


n»=^,-2?. 


IT 


ir»=2 , 


,m«=l^.=2© 




X» 


,r^=^,=2h. 


ir»««=cJ4 




IT* 


^=2®3 


^*«>=OPo 




'^=?,=29, 









M = present modulus of light at Sun's surface = 2204*95 
X Earths semiaxis major. I have already shown the im- 
portance of this quantity, (1) by identifying the velocity of 
light with the limiting velocity toward which the mean solar 
centrifugal and centripetal forces both tend, (2) by showing 
that the same harmonic progression is manifested in the Fraun- 
hofer lines and in planetary distances, (3) by tracing numerous 
harmonic arrangements among spectral lines of chemical ele- 
ments. M is the common dividend for all the planetary posi- 
tions; the combinations of various powers of ir and n are 
divisors. 

7r = ratio of circumference to diameter, and also, as I have 

shown, ratio of incipient to complete dissociative force. 
2 
n=: Q^rt-To =11*65684*. I propose to call this quantity 

^^ Gummere's criterion," because I obtained it by a calculation 
which was first suggested by a criticism of Samuel J. Gum- 
mere, late President of Haverford College. The criticism, 
together with Ennis's rejoinder, may be found in Appendix II. 
to ' Origin of the Stars.' 

• PhiL Mag. October 1877. 



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364 Prof. P. E. Chase on the Nebular HypotJieeis. 

Pq = Sun's present nebular radius^ or the distance at which 
planetary revolution and solar rotation would be synchronous. 

The subscript figures denote apsidal positions : i, secalar 
perihelion ; ,9 mean perihelion ; s^ mean ; 4, mean aphelion ; 
0, secular aphelion. 

The multiple 2 denotes the primitive nebular radius which 
would give the vis viva of circular-orbital revolution^ by con- 
densation to the present planetary radius vector. 

It should be noted: — that critical positions of all the planets, 
together with some asteroidal positions, are represented in the 
Table ; that all the symmetrical combinations of 7r and n, which 
are embraced in the Table, have planetary representations ; 
that both of these rupturing-factors seem to have been simul- 
taneously operative ; that, after the firot conversion of linear 
into circular motion, the exponential increments of ir form a 
figurate series ; and that the relations have all been found, not 
by happy guessing, but by following indications which are 
mathematically deducible from the necessary action of central 
forces. 

The character of the accordances is shown in the following 
Table:— 



Diyisor of 
M. 


Quotient. 


Fact, 


Minimum 
error. 


Maximum 
error. 


1F% 


60-210 
19165 

5165 

1-644 
1^942 

1-892 

730 
•167 


2\|r, 60068 
( $. 19-184 
'2^5 19-078 
r V, 6-203 

[2(m) 5-168 

^, 1-644 
2®. 1-932 
/ da 1-403 
125, 1-396 
/ ?, -723 
12$, -774 
OPo -167 


+ 142 
-•019 
+•087 
-•038 

-•003 

•000 
+•010 
—Oil 
-•004 
+•007 
-•044 

■000 


+'142 
-•019 
+•087 
-•088 

-•003 

+ 120 
-•068 
-132 
—054 
+•007 
-■044 
•000 


»»» 


»n> 

ir»ii« 

x*n 

n» 


xT 


ir*n* 



The importance of my introduction of various apsides into 
the study of planetary harmonies has been ftdly recognized 
by Alexander, the ^Nestor of harmonic astronomy; but in 
order to avoid all possible cavil I give the maximum errors^ or 
deviations from the semiaxis major, as well as the minimum 
errors, or deviations from the nearest apsis. 

The next Table gives the results of internal rupture which 
are indicated by Gummere's criterion, starting from the theo- 
retical origin of Neptune's present orbital vis viva* In each 
instance £e theoretical angular velocity of revolution, for the 



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Prof. P. E. Chaae on the Nebular Hypotliem. 365 

dense inner planet^ must have been (11*65684)^ times as great 
as the angtilar velocity of the nndisturbed portions of the gasi- 
form rotating nebnia. The common divisor for the quantities 
in the dividend column is n. 



Dividend. 


Quotient. 


Fact 


2*^* 


6-204 

2-576 

1-760 
1-6461 
1-637; 
-931 
•779 
•749 
•473 
^446 


5-203- V, 

2-677 (S) 

1-736 <ra 

1644 i, 

•982 e^ 
•774 ?, 
•749 $4 
•477 5, 
•455 ?, 


V. 


*• 

A, 


1* . . 


2®'. ... 


2»! 


h.t 


h! . 


3i. . 


2*.... 





The great density of Jupiter as compared with Neptune^ 
the great density of the intra-asteroidal as compared with the 
extra-asteroidal planets^ the position of Earth in the centre 
of the belt of greatest planetary condensation, the rupturing- 
relation (n) between the positions of Jupiter's incipient and 
Earth's complete condensation, the fact that Jupiter is the 
largest extra-asteroidal, while Earth is the largest intra-aste- 
roidal planet, the further evidence of a primeval intimate 
connexion between Jupiter and Earth which is furnished by 
the equivalence of their dissociation velocities, the probability, 
BO far as we can judge from Sun's present nebular radius (/Jq), 
that all the planets were formed when their orbital revolution 
was accomplished in less time than the rotation of the solar 
nucleus — aJl point to increments of wave-velocity and of cen- 
tripetal velocity as sources of interior nebular rupture, giving 
a new meaning to Herschel's doctrine of '^ subsidence," and 
making the inner moon of Mars a confirmation, rather than a 
formidable objection, to the nebular hypothesis. 

Adams and Leverrier found, as the result of their calcula- 
tions, that the disturbances of Uranus might be explained by 
the action of a planet, of a given size, in a certain position. 
The planet was found nearly in the direction indicated, but at 
three fourths of the anticipated distance, and having about 
three fifths of the anticipated magnitude. The laws of gravi- 
tation do not determine the reciprocal perturbations of cosmical 
orbs by a more inexorable mathematical necessity than that 
which connects the activities of M, ir, and n in an elastic me- 
dium like the hypothetical luminiferous SBther. 

The tendency to synchronous oscillations under tbe action 
of central forces, which Laplace, Peirce, and Kirkwood have 



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366 Prof. P. E. Chase on the Nebular Hypotheds. 

happily addaoed in explanation of some of their planetary 
harmonies is shown (1) in the synchronism of planetary revo- 
lution at Sun with the passage of a light-wave through the 
major axis of the Uranus-Earfh ellipse, (2) in the synchronism 
of solar rotation with the passage of a light-wave through the 
major axis of the modulus-atmosphere. 

The following Table represents theoretical stages of nebular 
condensation, based upon forces which are now operating 
within the solar system. It shows some new and interesting 
relations between three cardinal planetary centres, viz. the 
centre of greatest annular condensation (®), the centre of pla- 
netaiy inertia (h)^ and the centre of incipient systemic spe- 
cialization (^). 



r4-v 


p-^Po- 


p. 


Fact. 


E. 


2» 

3> 

4» 
214-86=»-i 
2049-61=1?, • 
646306=Tjr^ 


2* 
3* 

214-86* 
2049-61* 
646306* 


2-667 r, 

13-600r, 

42-667 fi 

46083-4 To 

932262 To 

4302218 To 


r2-667-{®, 
2-637= V3®j 
2-614= V.-i-» 
[2-780= h, "4- ir 
13-490= V2h, 
42-474= V2lir, 

46164-7 =214-86 
947611 =2M 
4263801 =9M=[«]-M» 


•000 

on 

•020 
043 
•001 
005 

•002 
016 
O09 



In this Table r^ = present solar nucleal radius ; r = past 
nucleal radius; r^ s= ^Earth's semiaxis major; po = present 
nebular radius ; p = past nebular radius ; B = ratio of error, 
found by dividing the difference between p and fact by p ; 
[*] = stellar distence with parallax (^'SO, which is of the 
same order of magnitude as the distance of a Centauri. It is 
further worthy of note, that Earth's position is a mean propor- 
tional between the nebular radius, wnen Sun's nucleus reached 
the Earth, and Sun's present surface ; that the nebular radius of 
the Jupiter-nucleal Sun was ^ of § of § of M ; that the nebular 
radius of the Uranus-nucleal Sun was nearly 5M (4*996 M); 
that the three outer nebular radii were thus in figurate pro- 

gression (2, 5, 9) ; and that M, when Sun was expanded to 
le outer portions of the asteroidal belt, was coincident with 
[*], the origin of the incipient wave-condensation of the ne- 
bular radius of the Neptune-nucleal Sun. 

The ratio (28 : 1) wnich I pointed out at the close of my 
paper on momentum and via viva*, and the important part 
which water plays in the armoury of our globe, suggest a 
comparison between the liguid and the vaporous states. The 

♦ Phil. Mag. October 1877. 



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On the Potential-diference produced hy Contact. 367 

elasticity of steam destroys its special centripetal tendency^ 
relatively to the earth, withont materially affecting the solar 
influence on its orbital motion ; and its volume is increased 
nearly in inverse ratio to the Sun's local attraction. 

Ganot* gives 1698 : 1 as the volume-ratio of steam at 100*^ 
G. to water at 0^ C, and he estimates the expansion of water 
befcwmi 0^ and IO(Pf sfc -046«+ '002584 s -049184. A nu- 
cleal expansion of 1*049184 corresponds to a nebular expan- 
sion of 1-049184*= 1-066; and 1698-r 1*066 = 1593, or very 
nearly n» (=1584). If Sun's mean distance is 93,000,000 
miles, the mean ratio of its attractive force upon Earth to 
Earth's equatorial gravitation is 1665. 



LI. On the Difference of Potential produced hy the Contact of 
different Substances. By Professor R. B. Clifton. 

To tlie Editors of the Philosophical Magazine and Journal. 

Gentlemen, 

IN the March Number of the Philosophical Magazine is 
published a letter from Professors Ayrton and Perry, in 
which they refer to my paper " On the Difference of Potential 
produced by the Contact of different Substances" (Proceedings 
of the Royal Society, vol. xxvi.). To this letter I have 
hitherto been prevented from making a reply ; but I now ven- 
ture to ask for the insertion in your Journal of a few remarks 
on some of the matters therein referred to. 

At the time my paper was written I was quite unaware of 
the investigation of the same subject which had been under- 
taken by Professors Ayrton and Perry ; and, indeed, the first 
information I obtained relative to their work was derived from 
the letter above mentioned. As soon as possible after the ap- 
pearance of their communication I endeavoured to find their 
paper, by searching through the various scientific periodicals 
and the publications of scientific societies, but without success. 
The title of the paper appeared in the ^ Report of the British 
Association,' but tne title only. 

As I was not present at the Meeting of the British Associa- 
tion at Glasgow, at which some account of the work of Pro- 
fessors Ayrton and Perry appears to have been given, but not 
reported, my ignorance of their work is, I hope, excusable, 
though I very much regret it. The paper in question has 
recently been read before the Royal Society, and it will, I 
believe, shortly be published. 

♦ Fifth Engl, ed., § 863. t Ibid. §§ 204-5. 

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368 Prof. R. B. CKfton on the Difference of Potential 

The nnsatisFactory nature of the explanatioii of voltaic action 
given in modem treatises on electricity has induced Profes- 
sors Ajrrton and Perr^ to undertake the investigation to 
which mey draw attention in their letter ; and the same cir- 
cumstance led me to give special attention to the subject; 
we even refer to the same passage in the textbook by Pro- 
fessor Fleeming Jenkin as an instance of statements requiring 
further explanation. It is therefore not extraordinary that 
there should be a great resemblance between the series of 
metals and liquids selected for examination by the two Profes- 
sors and by myself; but as they were working perfectly inde- 
pendent of mC; and I of them^ the claim of priority seems to 
be devoid of meaning. 

I shall not attempt to discuss the question of priority ; it is 
a matter in which I do not feel the slightest interest; but as 
Professors Ayrton and Perry state that 1 appear to have com- 
menced my earliest experiments on the subject several months 
after the Meeting of the British Association at Glasgow in 
1876, 1 think it better^ in order to avoid any diiSculty in the 
future, to- mention that I began to give special attention to 
this subject in 1874; and although frequent interruptions 
prevented me from making much progress, all the principal 
results communicated in my paper were obtained before the 
summer of 1876, and were introduced into my lectures deli- 
vered during Michaelmas Term 1876, and Hilary Term 1877. 
In my paper I have only given some of the latest quantitative 
determinations which I made — ^partly because I considered 
them the best, but more especiallv because I had, in making 
ihem, employed Clark's standard cell, to the variation of 
which I wished to draw attention. In my earlier experiments 
I had used a Daniell's cell. 

The method of investigating the difference of potential 
arising from the contact of different substances, employed by 
Professors Ayrton and Perry, is quite distinct from tnat which 
I adopted, so far at least as I am able to judge from the 
description without the drawing, which I have not yet seen. 

Their method, which seems to me both ingenious and novel, 
possesses the great advantage of permitting two liquids to be 
treated in the same way as two solids, or as a solid and a 
liquid. The method which I adopted is essentially the same 
as that employed by Kohlrausch in the case of two metals ; 
but the condenser was furnished with horizontal plates, for one 
of which a vessel of liquid could be substituted. The only 
changes which I introduced consist in the an^ngements for 
adjusting and moving the opposed plates, in the mode of in- 
sulating, and in the form of key used with the condenser. 



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produced by tJie Contact of different Substances. 369 

My apparatus enabled me not only to obsei*ye the sign of the 
difference of potential dae to metal-liquid contacts^ but also to 
obtain quantitative determinations ; as^ however, some of these 
differences of potential are very small; and a slight error in 
the construction of the condenser, which I believed to exist, 
would probably produce considerable errors in the values 
obtainea for the potentials, I thought it best not to introduce 
quantitative results in which I felt little confidence into my 
paper, which I onlv regarded as a preliminary notice. 

^tween most of the results obtained by Professors Ayrton 
and Perry and those published by myself, there is a fairly 
satisfactory agreement from a qualitative point of view ; but 
between such quantitative measures as admit of comparison 
there seem to be considerable descrepancies : these I trust 
will disappear when we introduce into our respective methods 
the improvements which we each admit to be necessary. 

Several of the criticisms on my paper, which have been 
introduced into the letter of Professors Ayrton and Perry, do 
not appear to me well founded ; but I must for want of time 
postpone the discussion of them; and possibly the more 
thorough investigation of the subject, which we each con- 
template, may render this discussion unnecessary. 

As the value of any results we may obtain m the future 
would be much increased by a ready means of comparison, I 
venture to suggest that we should adopt the same difference 
of potential as the unit. If I am right as to the variation in 
the difference of potential exhibited by the terminals of Clark's 
standard cell, it will clearly be undesirable to employ this cell; 
and I should suggest the use of the standard Daniell's cell 
referred to in my paper, viz. copper in a saturated solution of 
copper sulphate, and amalgamated zinc in a mixture of one 
part by weight of pure sulphuric acid and four parts by weight 
of distilled water. This cell seems to me to give a remarkably 
constant difference of potential when prepared on different 
occasions ; and the accurate expression of this difference, in 
volts, when obtained, would at once allow all our results to be 
translated into terms of the latter unit. 

I am, Gentlemen, 

Yours faithfully, 

R. B. Cliftok. 

Oxford, April 22, 1878. 



Phil. Mag. S. 5. Vol. 5. No. 32. May 1878. 2 B 

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[ 870 ] 

LIT. Problems relating to Unde rgr ound TempercUure. A 
Fragment. By Sir W. Thomson*. 

'PROBLEM I. — ^A fire is lighted on a small portion of an 
uninterrupted plane boundary of a mass of rock of the 
precise quality of that of Calton Hill, and after burning for a 
certain time is removed, the whole plane area of rock being 
then freely exposed to the atmosphere. It is required to deter- 
mine the consequent conduction of heat through the interior. 

Problem II. — It is required to trace the effect of an unosa- 
ally hot day on the internal temperature of such a mass of 
rock. 

Problem III. — It is required to trace the secular effect con- 
sequent on a sudden alteration of mean temperature. 

Problem IV. — It is required to determine the change of 
temperature within a ball of the rock consequent upon sud- 
denly removing it from a fluid of one constant temperature 
and plunging it into a fluid maintained at another constant 
temperature. 

Problems I., II., and III. In solving each of these prob- 
lems, we shall suppose the air in contact with the rock to be 
not sensibly influenced in its temperature by the conduction 
of heat inwards or outwards through the solid substance. In 
reality, the stratum of air in immeoiate contact with the rock 
must always have precisely the same temperature as the rock 
itself at its bounding surface ; and the continual mixing up of 
the different strata, whether by wind or by local convective 
currents due to differences of temperature, tends to bring the 
whole superincumbent mass of air to one temperature. Our 
supposition therefore amounts to assuming tnat the rate of 
variation of temperature from point to point m the rock near its 
surface, owing to the special cause under consideration, is much 
less than the ordinary changing variations from day to night. 
Hence, in Problems I., II., and III., the solutions will not be 
applicable until so much time has been allowed to elapse as 
will leave only a residual variation, small in comparison with 

* Communicated by the Author. An old MS., written eighteen veais 
ago and found today. It was kept back until the time should be K>und 
to write out the solutions of Proolems 11.. HE., and IV. The time was 
never found ; but as mere synthesis from tne solution of Problem I. suf- 
fices for II. and HI. (surface integration of the solution for I. over the 
medial plane solves II., and the time-integral from <8s -oo to ^=0, of the 
solution of n., gives that of III.), and as IV. is merely an example of 
Fourier's now well-known solution for the globe fsee Professors Ayrton 
and Perry's paper^ " On the Heat-conductivity of Stone," Philosophical 
Magazine for Apnl 1878), with numerical results calculated for trap-rock 
according to its thermal conductivity, as determined by the Edinburgh 
observations referred to in the fragment now published, the non-completion 
of the original proposal need not be much regretted. — W. T., March ^, 
1878. 



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Problems relating to Underground Tmnperature, 371 

the ordinarj diurnal maximum rates of increase and diminu- 
tion of temperatnre from point to point inwards in the imme- 
diate neighDoarhood of the snrfaoe. 

In the case of Problem 11. these conditions will be practically 
fulfilled^ and continue to be fulfiUed, very soon afker the day 
of extraordinary temperature of which the effect is to be con- 
sidered^ and we shall have a perfectly practiad solution illus- 
trative of the consequences experienoea several days or weeks 
later at the 3-foot and 6-foot aeep thermometers of the obser- 
vin^-station. The solution of Problem L, which we now pro- 
ceea to work out, will show clearly what dimensions as to 
space, time, and temperature may be chosen for a really prac- 
tical illustration of its conclusions. 

Problem I., subject to the limitations we have just stated, 
b equivalent to the following: — An infinitely smaU area of an 
infinite plane termiruUing on one Me a nuxss of uniform trap^ 
rock which extends up indefinitely in all directions on the other 
side J is it^nitely heated for an infinitely short time^ and the 
whole swrfdce is instantly and for ever after maintained at a 
constant temperature* It is required to determine the consequent 
internal variations of temperature. 

Let the solid be doubled so as to extend to an infinite dis- 
tance on both sides of the plane mentioned in the enunciation. 
This plane, when no longer a boundary, we shall call the medial 
plane. Let P, P' be two points equidistant from the medial 

Elane in a line perpendicular to it, on each side of the portion 
eated according to enunciation. Let a certain quantity of 
heat Q be suddenly created in an infinitely small portion of 
the solid round P, and at the same instant let an equal quan- 
tity be abstracted from an infinitely small portion of the solid 
round P'. The conseauent variations of temperaturo on the 
two sides of the medial plane of roference vnll be equal and 
opposite, bein^ a heating efiect which spreads from the medial 
plane in one du*ection, and a symmetrical cooling effect spread- 
ing from the same plane through the matter which we have 
imagined placed on its other side. The heating effect on the 
first side will, as is easily seen, be precisely the same as that 
proposed for investigation in Problem I.; and the thermal 
action of the mass we have supposed added on the other side 
will merolv have the effect of maintaining the temperaturo of 
the bounding plane unvaried. Now if a quantity Q of heat 
be placed at one point («, /9, 7) of an infinite homogeneous 
solid, the effect at any subsequent time ^ at any point x, y, z 
of the solid will be expressed by the formula 

. (>-«)«-^-(y- ^ )«^K*>Y)« 



2B2 



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872 Sir W- Thomson on Problems relattng 

discovered by Fourier : and Hie efieot of simultaneously fda- 
cing other quantities of heat, positive or negative, at other 
points will, as he has shown, be determined by finding the 
effect of each source separately by proper application of the 
same formula, and adding the results in accordance with the 
principle of the superposition of thermal conductions stated 
above. Hence the e£^ct of simultaneously placing equal po- 
sitive and negative quantities, +Q and ^Q, at two points, 
(a, )8, 7), (a', /S', y), will for any subsequent time t be ex- 
pressed by the formula 

^t-l{e- <. -.- - }. 

If in this expression we take aasia, a'=— 4^, )8=0, ff^Qj 
y=0, yssO, and suppose a to be infinitely small, we 
find what it becomes by differentiating the first term with 
reference to a, writing a instead of rfa, and taking a =0, /8=0, 
7=0, The result constitutes the solution of the pr<qpo8ed 
problem ; and thus, if v denote the required temperature at 
time t and point (^^y, z) of the solid, we find 

Qa s ^f5Ltl!±^« 

167rlAJ 

A more convenient formula* to express the solution will be 

* In this formula k denotes what I have called the thermal diffosiTity 
of the substance — ^that is to saj, its thermal conductivit j divided by the 
thermal capacity of unit bulk of the substance. Diffudvity is essentially 
reckoned in units of area per unit of time ) or, as Maxwell puts it, its di- 
mensions are j-^ T Its value (141 square British feet per aimum for Hie 

trap-rock of Galton Hill, used further on in the text) was taken from my 
paper on the *' Reduction of Observations of Underground Temperatur^" 
published in the Transactions of the Eoyal Society of Edinburgh uxt 
April 1860, where it was found by the application of Fourier's original 
formula to a harmonic reduction of Forbes's observations of underground 
temperature. Reducing this number to square centimetres per second, 
and expressizig similarly the results of my own reduction of Forbes's ob- 
servations for two other localities in the neighbourhood of Edinbui^h. 
and of Professor Everett's reductions of the Qreenwich Undergroand 
Observations, we have the following Table of diffusivitiee : — 

DiffuBivities. 

Trap-rock of Calton Hill "OOZSO of a square centim. per second. 

Sana of experimental warden .... *00872 „ „ „ 

Saodstone of CraigleiUi Quarry. . *02311 „ „ „ 

Gravel of Greenwich Observatory \ ./^t o,iq 
Hill |Ul-4» „ „ „ 

These numbers were first published by Everett, in his ^ Illustratioiia 
of the Centimetre-Gramme-Seoond (C. Gr. S) System of Units,' published 
by the Physical Society of London (1876), a most opportune and uaefiil 
publication. 



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to Underground Temperature. 873 

obtained by putting «'+y'+^=r^ and xssr cos 6. We thna 
have 

^- iS (*^^"'* ^^^ ^ • ^^"^^^ 

which expresses the temperature assumed at a time t after the 
application of the fire, by a point of the solid at a distance r 
from the point of the surface where the fire was applied, and 
situated in a direction inclined at an angle to tne vertical 
through this point. From this expression we conclude: — 

(1) The simultaneous temperatures at different points equi- 
distant from the position of the fire are simply proportional to 
the distances of tnese points from the plane surface. 

(2) The law of vanation of temperature with distance in 
any one line from the place where the fire was applied is the 
same at all times. 

(3) The law of variation of temperature with time is the 
same at all points of the solid. 

(4) Corresponding distances in the law of variation with 
distance increase in proportion to the square root of the time 
from the application and removal of the fire ; and therefore, 
of course, corresponding times in the law of variation with 
time are proportional to the squares of the distances. 

(5) The maximum value of the temperature, in the law of 
variation with distance, diminishes inversely as the square of 
the increasing time. 

' (6) The maximum value of the temperature in the law of 
variation with time, at any one point of the rock, is inversely 
as the fourth power of the distance from the place where the 
fire was applied. 

(7) At any one time subsequent to the application of the 
fire,.ui6 temperature increases in any direction from the place 
where the fire was applied to a maximum at a distance equal 
to \/2^^, and beyond that falls to zero at an infinite distance 
in every direction. The value of k for the trap-rock of Calton 
Hill being 141, when a year is taken as the unit of time and 
a British foot the unit of space, the radius of the hemispherical 
surface of maximum temperature is therefore 16*8 x s/t feet. 
Thus at the end of one year it is 16'8 feet, at the end of 
10,000 years it is 1689 feet, from the origin. The curve of 
fiff. 1 shows graphically the law of variation of temperature 
with distance. The ordinates of the curve are proportional to 
the temperatures, and the corresponding abscissas to the dis- 
^ces irom the origin or place of application of the fire. 

(8) At any one point at a finite distance within the solid 
(which, by hypothesis, is at temperature zero at the instant when 



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374 Problems rdating to Underground Temperature. 

the fire is applied and remoyed) the tempeiatare increaMS to a 
maximum at a certain time^ and then diminishes to zero again 

Fig.l. 



after an infinite time ; the ultimate law of diminution being in- 
versely as the square root of the fifth power of the time. The 
time when the maximum temperature is acquired at a distance 

r from the place where the fire was applied^ is j^rp or^ accord- 
ing to the value we have found for the trap-rock^ I^tT^ ^^ ^ 

year. Thus it appears that at one French foot from the place 
of the fire^ the maximum temperature is acquired a day and 
a half (more exactly 1*54 day) after the application and 
removal of the fire. At 15*4 French feet from the fire tiie 
maximum temperature is reached just a year from the begin- 
ning; and at 1540 feet the maximum is reached in 10^000 
years. The law of variation of temperature with time is shown 
by the curve of fig, 2, the ordinates of which represent tem- 
peratures^ and the abscissas times. 

Fig. 2. 



From these results we can readily see how the circumstances 
of the proposed problem may be actually realized^ if not riffo- 
rously, yet to any desired degree of approximation^ in the 
manner supposed — ^namely^ by keeping a nre burning for a cer- 
tain time over a small area of rock^ and then removmg it and 
oooling the surface. 

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[ 375 ] 

LIII. On the Electric Conductivity and Electrolysis of Chemical 
Compounds* By Dr. L. Bleekrods*. 

HITTOBF states^ as a result of his investigations on eleo- 
trolysist, that electrolytes are characterized by corre- 
sponding ions in them being capable of replacing one another. 
They are consequently salts in the sense attached to the term 
by modem chemistry ; and during electrolysis exchange takes 

Slaoe between the same constituents of their molecules as in 
ouble elective affinity. With the difficulty of this exchange 
he connects the resistance of the electrolytes to electrical con- 
daction; so that on this account water^ for example, and 
pmssic acid are such bad conductors. In Magnus's theory t 
the replaoeability of hydrogen by other substances is especially 
tsken into consideration. It tlierefore appeared to me desi- 
rable both to test the consequences deduced from HittorFs 
experiments and to try whether the presence of hydrogen 
replaceable in the compound either by metals or atomic groups 
(radicals) is connected with capability of electrolysis. If so^ 
ti^e latter should be absent when the above-mentioned chemical 
exchange does not take place. I selected the simplest com- 
pounds which could be preserved liquid without a solvent : to 
this category belong, of course, the condensed gases and also 
a great number of bodies derived from organic chemistry, as, 
for instance, the organo-metallic radicals, the substitution- 
products of ammonia, &c. Up to the present time very few 
organic substances have been thus investigated with respect 
to their electrolyzability ; and therefore I thought it would 
not be unimportant to supply this deficiency. 

1. Arrangement of the Experiments. 

The material available for these experiments was rather 
limited, as I had to select compounds containing either a metal 
or hydrogen, and which could also be kept in me liquid state, 
whether directly or by high pressure, as the gases, or by raising 
their temperature. Forme condensed gases it was most con- 
venient to employ Faraday's method. They were therefore 
enclosed in stout tubes of glass, into the two ends of which 
annealed platinum wires were fused to serve as electrodes. 
One of these traversed the entire length. of the tube to within 
1, 2, or 3 millims. of the other. They were separated by a 
layer of the liquid ; and by this arrangement conduction along 
the glass was almost entirely prevented. The other substances, 

.« Communicated by the Author. 

, ,t Pogg. Ann, vol. cvi. 1862. J Ibid. vol. cii. 1867. 



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376 Dr. L. Bleekrode on the Electric Conductivity 

not needing any high pressure to liquefy tbem^ were enclosed 
in short straight tubes ; so that small quantities sufficed. The 
conductivity of the electrolyzed substances was estimated f5rom 
the deflections of the needle of a galvanometer the coil of which 
was of thin wire, and in which the current from a couple of 
wires, zinc and silver, immersed in distilled water gave a de- 
flection of 5^, and of two silver wires in water, which were 
inserted in the circuit, a deflection of 2^. The current for 
the experiments on electrolysis was generated by: — first, a 
galvanic battery of twenty large Bunsen-Deleuil elements ; 
secondly, a battery of forty elements, which liberated in the 
voltameter 600 cubic centims. of oxyhydrogen gas per minute; 
and, thirdly, a battery of eighty elements, which produced 
840 cubic centims. per minute. Other series of experiments 
were made with induction-currents: for these I used a Ruhm- 
korff's induction-coil with a spark-length of 15 millims., and 
a second, the spark of which attained a length 42-70 millims. 

No currents of such intensity have, to my knowledge, been 
employed for electrolytic purposes, especially with uie sub- 
stances investigated by me, except in the experiments of 
Lapschin and Echanowitsch *. Warren De la Rue's chloride- 
of-silver battery furnishes currents of far greater intensity ; 
my experiments with it shall be discussed in a separate section. 

The current was led through the liquid and at the same time 
through the galvanometer ; but it might be questioned whether 
the deflection was not conditioned by conduction of the cur- 
rent in the glass tube f^ and by a metallic, not an electrolytic 
conduction. In order to determine what was the amount (if 
any) of conduction along the glass, if the galvanometer showed 
only a slight deflection, the liquid was removed from between 
the electrodes by inverting the tube ; the circuit could then be 
closed only by the glass sides. The deflection now produced 
I have named the glass-conduction. As, with the exception 
of alloys, no experiments had shown that compound substances 
conduct in metallic fashion only, and not at the same time 
electrolytically, I thought I could infer from the deflection of 
the galvanometer, not only the conductivity of the compound, 
but also its liability to electrolysis, although for the most part 
I could not observe any polarization-current. 

2. Electrolysis of Water, 

All the experiments which have been, made, and especiallj'^ 
the more recent observations of Kohlrausch, prove that water 

* BuU. de VAcad, de St. Fitersh. vol. iv. 1861 j Phil, Mag. [R^] 
vol. xxii. p. 808. 

t Couf. Beets, Pogg. Arm, vol. xcii. p. 465. 



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oni JElectrolyaU of Chemical Compounds, 877 

and alcohol, when as pnre as possible, are almost non-conduc- 
tors of the onrrent. Lapschin and Tichanowitsch also found 
that alcohol did not conduct the current of 1000 elements unless 
it had absorbed moisture. 

These two bodies, which at all events belong to the class of 
bad conductors, show that even the presence of hydrogen 
which is readily interchanged with metals does not always 
imply a sufficient conduction for electrolysis. In both we can 
make a direct substitution of potassium and sodium for hy- 
drogen ; and in water we can replace the hydrogen by iron ; 
and yet this property does not seem in this case to possess any 
special signihcance for the conduction. Even elective affinity 
appears here to take no part therein ; otherwise the electro- 
lysis of these substances could not be so doubtful, since several 
reactions are known in which they exchange their constituents 
— e. ff. water with oxide of potassium, water with alcoholates*, 
consequently in both cases with electrolytes.. With alcohol, 
however, decomposition by the metallic c&lorides, for example, 
requires the application of heat. 

3. Electrolyda of liquefied Hydrogen Acids. 

The combination of hydro^n with the metalloids (chlorine, 
bromine, iodine, sulphur, &oi) furnishes bodies the electrolysis 
of which was specially important for the purpose of this inves- 
tigation, since they exhibit numerous chemical reactions, and 
nearly all of them had only been tested hitherto, as to their 
electrolyzability, dissolved in water. As they are all gaseous, 
it was necessary to condense them. 

Faraday's method proved here the most suitable ; it gives 
with tolerable facility a sufficient quantity of great purity. 
The process of condensing the hydride of chlorine was as 
follows : — ^After a platinum wire had been fused into one end 
of a strong glass tube, reaching to the other extremity, con- 
centrated sulphuric acid was poured in till the tube was half 
filled, upon which, separated by a small disk of blotting-paper, 
was placed a layer of crystals of chloride of ammonium. 
Further, the second extremity of the tube was bent round, 
and into it a short platinum wire was inserted to serve as the 
second electrode, and, the tube being closed by f^^i^? fixed 
at a distance of 2 or 3 millims. from the first wire. The two 

* In this case the reaction is : — 

This alcohnlate is an electrolyte ; with the battery of 20 Bunsen's ele- 
ments a rapid evolution of gas took place^ while the* liquid became brown- 
coloured. 



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378 Dr. L. Bleekrode an the EUetrie Conductivity 

wires were ccmseqaently never ooimected with ihe same part 
of the tube, so that oondoction along the glass was rendered 
difficnlt. By agitation and suitable motion the substances for 
the production of the gas were now brou^t into contact ; 
and the action was assisted by moderate heating; e^ieeial care 
was necessary to prevent the products of decomposition from 
beinff brought over by the gas. In all the experiments I 
finaify succeeded in collecting in the bent part of the tube a 
quantity of perfectly pure liquefied gas. The liquid sulphide 
of hydrogen was prepared from sulphide of iron and dilute 
sulphuric acid; hydriodic acid from a mixture of iodine, 
iodide of potassium^ and moistened red phosphorus ; hvdro* 
bromic acid from liquid bromine and a mixture of bromide of 
potassium and moistened red phomhorus ; arseniuretted 
nydrogen from arsenide of zinc and oiluted sulphuric acid ; 
hydrocyanic acid from cyanide of mercury by decomposition 
with sulphuric acid and cooling. A small quantity of chloride 
of calcium or pure lime was introduced into the tube^ near 
the bent portion^ to dry the gas as it was formed. The re- 
suits of me experiments with these substances are contained 
in the following Table, in which D signifies the deflection of 
the fi^vanometer-needle on the passage of the current through 
the uquid, and G the deflection corresponding to tiie conduc- 
tion along the glass : — 

Table I. 



} 



Com- 
pound. 


QalTUiio battery. 


Induction-ooiL 




20Buiis«n'B 
elements. 


40Bunflen'a 

dements. 


SparkH^isoh. 
*-15millims. 


[Spark-disch. 
ss70millims 


Bemarks. 


Hca 


D.6 


G-8 
D- 


D=.|» 


D«l8 


Spark-disohaige in tlie 
liquid, and the tube 
shatteied. 


HBr ... 


D- 8 


G» 8 

D- 3 . 


D-0 


D- 8 


Spark-disoharge, and 
ttie tube shattered. 


m 


D= 


G- 


D-0 


D- 6 


Heat eTolTed and 


H.S 


B- 


D- 
G- 
D- 


D-0 


D- 6 


iodine araarated. 

deraUe erolution ol 
heat, tube shattered. 


H,A9... 




G» 
D- 


D-Ot 




No discharge; distance